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Javier E

Elusive 'Einstein' Solves a Longstanding Math Problem - The New York Times - 0 views

www.nytimes.com/...thematics-tiling-einstein.html

math problem solution history research

shared by Javier E on 30 Mar 23 - No Cached
  • after a decade of failed attempts, David Smith, a self-described shape hobbyist of Bridlington in East Yorkshire, England, suspected that he might have finally solved an open problem in the mathematics of tiling: That is, he thought he might have discovered an “einstein.”
  • In less poetic terms, an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”)
  • Your typical wallpaper or tiled floor is part of an infinite pattern that repeats periodically; when shifted, or “translated,” the pattern can be exactly superimposed on itself
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  • An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. This is known as the einstein problem.
  • black and white squares also can make weird nonperiodic patterns, in addition to the familiar, periodic checkerboard pattern. “It’s really pretty trivial to be able to make weird and interesting patterns,” he said. The magic of the two Penrose tiles is that they make only nonperiodic patterns — that’s all they can do.“But then the Holy Grail was, could you do with one — one tile?” Dr. Goodman-Strauss said.
  • now a new paper — by Mr. Smith and three co-authors with mathematical and computational expertise — proves Mr. Smith’s discovery true. The researchers called their einstein “the hat,
  • “The most significant aspect for me is that the tiling does not clearly fall into any of the familiar classes of structures that we understand.”
  • “I’m always messing about and experimenting with shapes,” said Mr. Smith, 64, who worked as a printing technician, among other jobs, and retired early. Although he enjoyed math in high school, he didn’t excel at it, he said. But he has long been “obsessively intrigued” by the einstein problem.
  • Sir Roger found the proofs “very complicated.” Nonetheless, he was “extremely intrigued” by the einstein, he said: “It’s a really good shape, strikingly simple.”
  • The simplicity came honestly. Mr. Smith’s investigations were mostly by hand; one of his co-authors described him as an “imaginative tinkerer.”
  • When in November he found a tile that seemed to fill the plane without a repeating pattern, he emailed Craig Kaplan, a co-author and a computer scientist at the University of Waterloo.
  • “It was clear that something unusual was happening with this shape,” Dr. Kaplan said. Taking a computational approach that built on previous research, his algorithm generated larger and larger swaths of hat tiles. “There didn’t seem to be any limit to how large a blob of tiles the software could construct,”
  • The first step, Dr. Kaplan said, was to “define a set of four ‘metatiles,’ simple shapes that stand in for small groupings of one, two, or four hats.” The metatiles assemble into four larger shapes that behave similarly. This assembly, from metatiles to supertiles to supersupertiles, ad infinitum, covered “larger and larger mathematical ‘floors’ with copies of the hat,” Dr. Kaplan said. “We then show that this sort of hierarchical assembly is essentially the only way to tile the plane with hats, which turns out to be enough to show that it can never tile periodically.”
  • some might wonder whether this is a two-tile, not one-tile, set of aperiodic monotiles.
  • Dr. Goodman-Strauss had raised this subtlety on a tiling listserv: “Is there one hat or two?” The consensus was that a monotile counts as such even using its reflection. That leaves an open question, Dr. Berger said: Is there an einstein that will do the job without reflection?
  • “the hat” was not a new geometric invention. It is a polykite — it consists of eight kites. (Take a hexagon and draw three lines, connecting the center of each side to the center of its opposite side; the six shapes that result are kites.)
  • “It’s likely that others have contemplated this hat shape in the past, just not in a context where they proceeded to investigate its tiling properties,” Dr. Kaplan said. “I like to think that it was hiding in plain sight.”
  • Incredibly, Mr. Smith later found a second einstein. He called it “the turtle” — a polykite made of not eight kites but 10. It was “uncanny,” Dr. Kaplan said. He recalled feeling panicked; he was already “neck deep in the hat.”
  • Dr. Myers, who had done similar computations, promptly discovered a profound connection between the hat and the turtle. And he discerned that, in fact, there was an entire family of related einsteins — a continuous, uncountable infinity of shapes that morph one to the next.
  • this einstein family motivated the second proof, which offers a new tool for proving aperiodicity. The math seemed “too good to be true,” Dr. Myers said in an email. “I wasn’t expecting such a different approach to proving aperiodicity — but everything seemed to hold together as I wrote up the details.”
  • Mr. Smith was amazed to see the research paper come together. “I was no help, to be honest.” He appreciated the illustrations, he said: “I’m more of a pictures person.”
Javier E

Map Shows Where Sea Level Rise Will Drown American Cities | WIRED - 0 views

www.wired.com/...ise-will-drown-american-cities

climate change global warming sea level coastline cities research

shared by Javier E on 13 Oct 15 - No Cached
  • A new map from Climate Central shows how the water will flow into hundreds of US cities under the best and worst global warming scenarios
  • “One of the most astonishing things to me was finding that burning one gallon of gasoline translates to adding 400 gallons of water volume to the ocean in the long run,”
  • For example, when the global atmospheric CO2 level reaches 930 gigatons, Boston will be due for about 9 feet of sea level rise. That’s enough water to cover 25 percent of the city during high tide. In the extreme cuts scenario, atmospheric CO2 never reaches that level. Under business as usual fossil emissions however, a quarter of Boston is locked into a future under water by 2045.
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  • The study, in other words, isn’t about how much see level rise happens this century, but whether this century’s emissions bank enough carbon for total ice melt down—or some less drastic version. “Our analysis really looks at a 2000 year envelope,” says Strauss.
  • Under the ice, Greenland and Antarctica are uncharted territories. In order to calculate the rate at which those massive ice sheets slough off, Levermann says he would need to know more about the texture of the underlying rock.
B Mannke

Why Are Clowns Scary? | Psychology Today - 0 views

www.psychologytoday.com/...why-are-clowns-scary

shared by B Mannke on 11 Nov 13 - No Cached
  • But is coulrophobia a real fear? And, for that matter, what is fear?
  • Psychologists believe that this kind of fear may have less to do with clowns and more with the unsettling familiarity. A normal-sized body with a painted face, big shoes, colorful clothes—but what's under there?"People are typically frightened by things which are wrong in some way, wrong in a disturbingly unfamiliar way," says Paul Salkovskis of the Maudsley Hospital Centre for Anxiety Disorders and Trauma in London.Anthropologists may approach the phobia from the clown's perspective. In 1961, Claude Levi Strauss wrote about the "freedoms" that masking oneself allows. A mask gives a clown the chance to adopt a new identity: "the facial disguise," he writes, "temporarily eliminate[s] from social intercourse that part of the body which...the individual's personal feelings and attitudes are revealed or can be deliberately communicated to others."
Javier E

History News Network | Are You a Genius? - 0 views

historynewsnetwork.org/...159549

genius historiography France language psychology paradigm

shared by Javier E on 29 Jun 15 - No Cached
  • the real question is not so much ‘What is genius?’ or even ‘Who is a genius?’ but rather, ‘What stake do we have in the whole idea of genius?’ or even, ‘Who’s asking and what’s behind their question?’
  • These are the issues I address in my new book by looking at the different views and theories of genius over the course of three centuries, from the start of the eighteenth century to the present day.
  • I concentrated on France, partly because French literature and intellectual history happen to be my area of expertise and personal interest; partly because the French contribution to the literature on genius hasn’t received its due; but mostly because the variety and the inventiveness of the views and theories of genius in France was a story worth telling for itself
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  • For me it’s this literature, more than the phenomenon itself, which makes genius a topic worth paying attention to. And the more you read, the less likely you are to be able to come up with any definition of what genius might be.
  • For eighteenth-century commentators, genius was self-evident: you knew it when you saw it, but for the nineteenth-century Romantics, genius was essentially misunderstood, and only genius itself was capable of recognizing its own kind
  • After the French Revolution, the question of national genius (another sense of the word, deriving from the genius loci) was subject to particularly anxious or over-assertive scrutiny. A number of nineteenth-century novels allowed for a rare feminine role in genius, but almost always doomed genius to failure. The medical profession turned the genius into a madman, while the experimental psychologists at the end of the century devised the IQ test which made genius nothing more than a high point on a continuous scale of intelligence. Child prodigies were the stuff of children’s literature but real examples in the twentieth century generated skepticism about the whole notion of genius, until Julia Kristeva came along and rehabilitated genius as essentially feminine, and Jacques Derrida embraced imposture as its essential quality
  • What all this indicates is that the idea of genius is curiously labile, that it changes shape, definition and value according to the way it’s talked about, but also that there’s something about the idea that, as Claude Lévi-Strauss said about animals, makes it ‘good to think with.’        
Javier E

'The Fourth Turning' Enters Pop Culture - The New York Times - 0 views

www.nytimes.com/...ourth-turning-pop-culture.html

turning point history crisis culture book trend framework historiography cycles

shared by Javier E on 08 Jul 23 - No Cached
  • According to “fourth turning” proponents, American history goes through recurring cycles. Each one, which lasts about 80 to 100 years, consists of four generation-long seasons, or “turnings.” The winter season is a time of upheaval and reconstruction — a fourth turning.
  • The theory first appeared in “The Fourth Turning,” a work of pop political science that has had a cult following more or less since it was published in 1997. In the last few years of political turmoil, the book and its ideas have bubbled into the mainstream.
  • According to “The Fourth Turning,” previous crisis periods include the American Revolution, the Civil War and World War II. America entered its latest fourth turning in the mid-2000s. It will culminate in a crisis sometime in the 2020s — i.e., now.
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  • One of the book’s authors, Neil Howe, 71, has become a frequent podcast guest. A follow-up, “The Fourth Turning Is Here,” comes out this month.
  • The play’s author, Will Arbery, 33, said he heard about “The Fourth Turning” while researching Stephen K. Bannon, the right-wing firebrand and former adviser to President Donald J. Trump, who is a longtime fan of the book and directed a 2010 documentary based on its ideas.
  • He described it as “this almost fun theory about history,” but added: “And yet there’s something deeply menacing about it.”
  • Mr. Arbery, who said he does not subscribe to the theory, sees parallels between the fourth turning and other nonscientific beliefs. “I modeled the way that Teresa talks about the fourth turning on the way that young liberals talk about astrology,” he said.
  • The book’s outlook on the near future has made it appealing to macro traders and crypto enthusiasts, and it is frequently cited on the podcasts “Macro Voices,” “Wealthion” and “On the Margin.”
  • “I’ve read ‘The Fourth Turning,’ and indeed found it useful from a macroeconomic investing perspective,” Lyn Alden, 35, an investment analyst, wrote in an email. “History doesn’t repeat, but it kind of gives us a loose framework to work with.”
  • “The Fourth Turning” captured a mood of decline in recent American life. “I remember feeling safe in the ’90s, and then as soon as 9/11 hit, the world went topsy-turvy,” he said. “Every time my cohort got to the point where we were optimistic, another crisis happened. When I read the book, I was like, ‘That makes sense.’”
  • “The Fourth Turning” was conceived during a period of relative calm. In the late 1980s, Mr. Howe, a Washington, D.C., policy analyst, teamed with William Strauss, a founder of the political satire troupe the Capitol Steps.
  • Their first book, “Generations,” told a story of American history through generational profiles going back to the 1600s. The book was said to have influenced Bill Clinton to choose a fellow baby boomer, Al Gore, as his running mate
  • when the 2008 financial crisis hit at almost exactly the point when the start of the fourth turning was predicted, it seemed to many that the authors might have been onto something. Recent events — the pandemic, the storming of the Capitol — have seemingly provided more evidence for the book’s fans.
  • Historically, a fourth turning crisis has always translated into a civil war, a war of great nations, or both, according to the book. Either is possible over the next decade, Mr. Howe said. But he is a doomsayer with an optimistic streak: Each fourth turning, in his telling, kicks off a renaissance in civic life.
  • In the new book, he describes what a coming civil war or geopolitical conflict might look like — though he shies away from casting himself as a modern-day Nostradamus.
  • “This big tidal shift is arriving,” Mr. Howe said. “But if you’re asking me which wave is going to knock down the lighthouse, I can’t do that. I can just tell you that this is the time period. It gives you a good idea of what to watch for.”
peterconnelly

Opinion: Want to keep your employees happy? Offer these 5 things - CNN - 0 views

www.cnn.com/...index.html

shared by peterconnelly on 01 Jun 22 - No Cached
  • To attract workers in today's tight labor market, companies are touting better workplace amenities. Amazon is running ads about the company's pay and benefits. Levi Strauss is offering to cover travel costs for workers seeking abortions. Airbnb is allowing its employees to permanently work remotely. This is a workers' paradise in the making.
  • But they also made clear that willingness to stay with the current employer is also a matter of whether their direct managers can deliver on five other factors beyond the paycheck that keep people happy, productive and on the team.
  • Now, increasing numbers of people demand the ability to choose when, where and how to work.
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  • This made the employee feel like remote work was just another set of disempowering rules.
  • Workers clearly felt empowered by having more control over their own work life. Companies must give people choices that match their unique work and life needs.
  • People crave predictability. Surprises make it harder for employees to plan their lives and have peace of mind. When constant change is inflicted on them, without a chance to anticipate it or participate in decisions about it, people get anxious and passive, and dream of escape.
  • For instance, workers who get unexpected spot bonuses sometimes feel that they don't know what to count on when calculating their future compensation; they'd rather have a predictable total package.
  • People thrive when their value is acknowledged by getting more responsibility, recognition and stature, such as a bigger title.
  • Jobs that convey a sense of purpose and meaning are more likely to exercise an emotional hold on people. Whether or not the company overall thinks it stands for social responsibility, people want to see that chance to make a difference in their immediate work experience.
  • Conventional wisdom holds that the best way to improve employment circumstances is to get an offer from a new company. That shouldn't have to be the case. Managers who want to retain people should act as if they are just now hiring them.
  • The best labor pool could be the one companies already have. They should treat their people as a precious resource and give them what they want from work. Rewarding them will reward the business.
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