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The Covington Scissor Welcome to another controversy algorithmically designed to tear America apart.
In a short story published last October, “Sort by Controversial,” Scott Alexander imagines a Silicon Valley company that accidentally comes up with an algorithm to generate what it calls a “Scissor.” The scissor is a statement, an idea or a scenario that’s somehow perfectly calibrated to tear people apart — not just by generating disagreement, but by generating total incredulity that somebody could possibly disagree with your interpretation of the controversy, followed by escalating fury and paranoia and polarization, until the debate seems like a completely existential, win-or-perish fight.When you start arguing with someone over a Scissor statement, Alexander’s narrator explains, “at first you just think they’re an imbecile. Then they call you an imbecile, and you want to defend yourself. … You notice all the little ways they’re lying to you and themselves and their audience every time they open their mouth to defend their imbecilic opinion. Then you notice how all the lies are connected, that in order to keep getting the little things like the Scissor statement wrong, they have to drag in everything else. Eventually even that doesn’t work; they’ve just got to make everybody hate you so that nobody will even listen to your argument no matter how obviously true it is.”
NYTimes  controversies  racism 
6 minutes ago by thomas.kochi
Division and Its Discontents - The New York Times
There’s a narrative line that runs through arithmetic, but many of us missed it in the haze of long division and common denominators. It’s the story of the quest for ever-more versatile numbers.
The “natural numbers” 1, 2, 3 and so on are good enough if all we want to do is count, add and multiply. But once we ask how much remains when everything is taken away, we are forced to create a new kind of number — zero — and since debts can be owed, we need negative numbers too. This enlarged universe of numbers called “integers” is every bit as self-contained as the natural numbers, but much more powerful because it embraces subtraction as well.
A new crisis comes when we try to work out the mathematics of sharing. Dividing a whole number evenly is not always possible … unless we expand the universe once more, now by inventing fractions. These are ratios of integers — hence their technical name, “rational numbers.” Sadly, this is the place where many students hit the mathematical wall.
There are many confusing things about division and its consequences, but perhaps the most maddening is that there are so many different ways to describe a part of a whole.
math  nytimes  strogatz 
11 hours ago by rgl7194
The Enemy of My Enemy - The New York Times
It’s traditional to teach kids subtraction right after addition.  That makes sense — the same facts about numbers get used in both, though in reverse.  And the black art of “borrowing,” so crucial to successful subtraction, is only a little more baroque than that of “carrying,” its counterpart for addition.  If you can cope with calculating 23 + 9, you’ll be ready for 23 – 9 soon enough.
At a deeper level, however, subtraction raises a much more disturbing issue, one that never arises with addition.  Subtraction can generate negative numbers.  If I try to take 6 cookies away from you but you only have 2, I can’t do it — except in my mind, where you now have negative 4 cookies, whatever that means.
Subtraction forces us to expand our conception of what numbers are.  Negative numbers are a lot more abstract than positive numbers — you can’t see negative 4 cookies and certainly can’t eat them — but you can think about them, and you have to, in all aspects of daily life, from debts and overdrafts to contending with freezing temperatures and parking garages.
math  nytimes  strogatz 
11 hours ago by rgl7194
Rock Groups - The New York Times
Like anything else, arithmetic has its serious side and its playful side.
The serious side is what we all learned in school: how to work with columns of numbers, adding them, subtracting them, grinding them through the spreadsheet calculations needed for tax returns and year-end reports. This side of arithmetic is important, practical and — for many people — joyless.
The playful side of arithmetic is a lot less familiar, unless you were trained in the ways of advanced mathematics. Yet there’s nothing inherently advanced about it. It’s as natural as a child’s curiosity.
In his book “A Mathematician’s Lament,” Paul Lockhart advocates an educational approach in which numbers are treated more concretely than usual: he asks us to imagine them as groups of rocks. For example, six corresponds to a group of rocks like this...
math  nytimes  strogatz 
11 hours ago by rgl7194
From Fish to Infinity - The New York Times
I have a friend who gets a tremendous kick out of science, even though he’s an artist. Whenever we get together all he wants to do is chat about the latest thing in evolution or quantum mechanics. But when it comes to math, he feels at sea, and it saddens him. The strange symbols keep him out. He says he doesn’t even know how to pronounce them.
In fact, his alienation runs a lot deeper. He’s not sure what mathematicians do all day, or what they mean when they say a proof is elegant. Sometimes we joke that I just should sit him down and teach him everything, starting with 1 + 1 = 2 and going as far as we can.
Crazy as it sounds, over the next several weeks I’m going to try to do something close to that. I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.
So, let’s begin with pre-school.
math  nytimes  strogatz 
11 hours ago by rgl7194
The Joy of X - The New York Times
Steven Strogatz on math, from basic to baffling.
At this stage in the series it’s time to shift gears, moving on from grade school arithmetic to high school math.
Over the next few weeks we’ll be revisiting algebra, geometry and trig.  Don’t worry if you’ve forgotten them all — there won’t be any tests this time around, so instead of worrying about details, we have the luxury of concentrating on the most beautiful, important and far-reaching ideas.
From Fish to Infinity (Jan. 31, 2010)
Rock Groups (Feb. 7, 2010)
The Enemy of My Enemy (Feb. 14, 2010)
Division and Its Discontents (Feb. 21, 2010)
Algebra, for example, may have once struck you as a dizzying mix of symbols, definitions and procedures, but in the end they all boil down to just two activities — solving for x and working with formulas.
Solving for x is detective work.  You’re searching for an unknown number, x.  You’ve been handed a few clues about it, either in the form of an equation like 2x + 3 = 7, or, less conveniently, in a convoluted verbal description of it (as in those scary “word problems”).  In either case, the goal is to identify x from the information given.
math  nytimes  strogatz 
11 hours ago by rgl7194
Opinion | Trump Tries to Destroy, and Justice Roberts Tries to Save, What Makes America Great - The New York Times
Our institutions give us strength. Fortunately, people with civic courage are working to protect them.
For me, the most disturbing thing about the Trump presidency is the way each week, like a steady drip of acid, Donald Trump tries to erode the thing that truly makes us great as a country and the envy of so many around the world — the independence and nonpartisan character of our courts, our military, our F.B.I., our Border Patrol and our whole federal bureaucracy.
No modern president has been more willing to use U.S. service members or border police as props for his politics, to blithely declare without evidence that most of the 800,000 federal workers going unpaid during the government shutdown are Democrats, to refer to the Pentagon leadership as “my generals” and “my military,” and to denounce different federal judges who have ruled against him as a “so-called judge,” an “Obama judge” and a “Mexican” judge (even though he was born in Indiana).
Why is this so important? Because America’s core governing institutions were not built to be “conservative” or “liberal.” They were built to take our deepest values and our highest ideals and animate them, promote them and protect them — to bring them to life and to scale them. They are the continuity that binds one generation of Americans to the next and the beacon for how we work together to build an ever more perfect union.
At their best, these institutions have created the regulatory foundations and legal and security frameworks that have made America great — that have enabled innovation to be sparked, commerce to flourish and ideas to freely blossom. Rather than serving any party or person’s whims, these institutions have promoted and protected enduring American values, laws, norms and ideals.
trump  gov2.0  shutdown  SCOTUS  politics  nytimes  op-ed 
11 hours ago by rgl7194
Visualizing Vastness - The New York Times
This is the final essay in a six-part series.
In the funky, crunchy, slightly gritty college town where I live, we have a pedestrian mall called the Ithaca Commons. You can probably picture it: A gem store. A hemp shop. Lots of places to buy hand-made candles.
And a scale model of the solar system … five billion times smaller than the real thing.
Built in honor of Carl Sagan, the Cornell astronomer, author and science communicator, the Sagan Planet Walk offers lessons that reach far beyond astronomy. It’s a case study in visualizing vastness.
Admit it. You have no real feeling for the size of the solar system. That’s O.K. Nobody else does either. Even knowing the numbers doesn’t help much. If I tell you the Earth is about 8,000 miles in diameter and 93,000,000 miles from the Sun, does that give you any sense of the distances involved? No, because the numbers are too big. Things that are so far removed from our daily experience — like quarks, and dinosaurs, and Kim Kardashian — are inherently hard to understand.
math  nytimes  strogatz 
12 hours ago by rgl7194
Dangerous Intersection - The New York Times
I don’t know much about camels, having ridden one only once (and that was enough). But from what I’ve been told, you can usually add another piece of straw to a camel’s burden without ill effect.
Except, of course, when it’s the last straw.
The ancient proverb about the straw that broke the camel’s back is meant as a lesson about the nature of precipitous change. It reminds us that big changes don’t necessarily require big forces. If the conditions are just right (or wrong), a tap can push a system over the brink.
In the mid-20th century, mathematicians updated this proverb by turning it into a picture, a graph of the interplay between input and output, force and response. A field known as catastrophe theory explores how slow continuous changes in the force applied to a system (like the gradually increasing load on a camel’s back) can trigger rapid discontinuous jumps in its response.
math  nytimes  strogatz 
12 hours ago by rgl7194
It's My Birthday Too, Yeah - The New York Times
By an amazing coincidence my sister, Cathy, and my Aunt Vere have the same birthday: April 4.
Actually, it’s not so amazing. In any extended family with enough siblings, aunts, uncles and cousins, you’d expect at least one such birthday coincidence. Certainly, if there are 366 people in the family — more relatives than days of the year — they can’t all have different birthdays, so a match is guaranteed in a family this big. (Or if you’re worried about leap year, make it 367.)
But suppose we don’t insist on absolute certainty. A classic puzzle called the “birthday problem” asks: How many people would be enough to make the odds of a match at least 50-50?
The answer, just 23 people, comes as a shock to most of us the first time we hear it. Partly that’s because it’s so much less than 366. But it’s also because we tend to mistake the question for one about ourselves. My birthday.
John Allen Paulos gave a vivid example of this error in his trenchant best seller “Innumeracy”...
math  nytimes  strogatz 
12 hours ago by rgl7194
Proportion Control - The New York Times
No other number attracts such a fevered following as the golden ratio. Approximately equal to 1.618 and denoted by the Greek letter phi, it’s been canonized as the “Divine Proportion.” Its devotees will tell you it’s ubiquitous in nature, art and architecture. And there are plastic surgeons and financial mavens who will tell you it’s the secret to pretty faces and handsome returns.

Not bad for the second-most famous irrational number. In your face, pi!

It even made a cameo appearance in “The Da Vinci Code.” While trying to decipher the clues left at the murder scene in the Louvre that opens the novel, the hero, Robert Langdon, “felt himself suddenly reeling back to Harvard, standing in front of his ‘Symbolism in Art’ class, writing his favorite number on the chalkboard. 1.618.”

Langdon tells his class that, among other astonishing things, da Vinci “was the first to show that the human body is literally made of building blocks whose proportional ratios always equal phi.”
math  nytimes  strogatz 
12 hours ago by rgl7194
Friends You Can Count On - The New York Times
You spend your time tweeting, friending, liking, poking, and in the few minutes left, cultivating friends in the flesh. Yet sadly, despite all your efforts, you probably have fewer friends than most of your friends have. But don’t despair — the same is true for almost all of us. Our friends are typically more popular than we are.
Don’t believe it? Consider these results from a colossal recent study of Facebook by Johan Ugander, Brian Karrer, Lars Backstrom and Cameron Marlow. (Disclosure: Ugander is a student at Cornell, and I’m on his doctoral committee.) They examined all of Facebook’s active users, which at the time included 721 million people — about 10 percent of the world’s population — with 69 billion friendships among them. First, the researchers looked at how users stacked up against their circle of friends. They found that a user’s friend count was less than the average friend count of his or her friends, 93 percent of the time. Next, they measured averages across Facebook as a whole, and found that users had an average of 190 friends, while their friends averaged 635 friends of their own.
Studies of offline social networks show the same trend. It has nothing to do with personalities; it follows from basic arithmetic. For any network where some people have more friends than others, it’s a theorem that the average number of friends of friends is always greater than the average number of friends of individuals.
math  nytimes  strogatz 
12 hours ago by rgl7194
Singular Sensations - The New York Times
Sharpen your pencils, dust off your abacus and join me once again for a few weeks of mind-bending pleasure. No, I’m not speaking about politics.
We’ll travel to a place where problems have answers and truth exists.
The haven of mathematics.
My previous series offered a panoramic view of the field. This time, in “Me, Myself and Math,” we’ll focus on how the subject I love — math — relates to the subject we all love — ourselves.
From the DNA that encodes us, to the fingerprints that characterize us, to our place in the universe and our friend counts on Facebook, we are mathematical marvels. In the coming weeks we’ll see what math can reveal about us and our world, and at the same time, how the wonders of us have inspired advances in math. No specialized knowledge or background will be required, just curiosity and a sense of fun.
math  nytimes  strogatz 
12 hours ago by rgl7194
Numberplay: Steven Strogatz and The Joy of x, Part 2 - The New York Times
This week we offer a second puzzle from “The Joy of x,” the recently-released book by mathematician Steven Strogatz based on his popular New York Times Opinionator Series “The Elements of Math.” If you happened to enjoy “The Elements of Math,” you’ll love “The Joy of x.”
Also this week — if you happen to be in Manhattan (and can get a ticket!), you can see Steven Strogatz in person. Dr. Strogatz will be presenting “Doing Math in Public,” an account of his adventures as a New York Times columnist bringing the joy and beauty of math to the general public. The talk will take place at Baruch College and is sponsored by The Museum of Mathematics as part of its Math Encounters series.
math  books  puzzle  strogatz  nytimes 
12 hours ago by rgl7194
Numberplay: Steven Strogatz and the Joy of x - The New York Times
We have a special treat this week and next: puzzles from Steven Strogatz‘s “The Joy of x,” the recently-released book based on Dr. Strogatz’s popular New York Times Opinionator Series “The Elements of Math.” (“The Elements of Math,” in case you missed it, is Dr. Strogatz’ 15-part series on mathematics from “the basic to the baffling” that ran back in early 2010.)
I loved “The Joy of x.” The book offers effortless access to the real beauty and coherence of math. If Dr. Strogatz were a performing jazz musician, he’d invite you up on stage, give you an instrument, and have you experience the music flowing through you. “The Joy of x” is like that.
And if you’re in Manhattan on Dec. 5 you will have the opportunity to experience this jazz firsthand. Dr. Strogatz will be presenting “Doing Math in Public” as part of the Math Encounters series presented by the Museum of Mathematics. Details at the end of this post.
math  books  strogatz  puzzle  nytimes 
12 hours ago by rgl7194
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Steven Strogatz on the Elements of Math
math  nytimes  search  strogatz 
12 hours ago by rgl7194
Opinion | Beware the Furies, President Trump - The New York Times
WASHINGTON — After I’d been writing a column for a few years, a male boss gave me a T-shirt depicting the Furies swooping.
He didn’t mean it as a compliment.
The three sisters, the “infernal goddesses” of ancient mythology born from the blood shed by Uranus when he was castrated by his son, were known for relentlessly hounding men. But the Furies took vengeance on wicked men who hurt women and swore false oaths.
So I took it as a compliment.
The capital has suddenly been infused with the spirit of the Furies. After many false springs and discouraging backlashes, we are finally experiencing a revolutionary assertion of women’s power that is transforming Congress.
“Kill Bill”-style, the fiery Democratic women keep coming, driven by vengeance against the wicked man in the White House with the history of hurting women and swearing false oaths.
gov2.0  politics  congress  women  trump  AOC  nytimes 
13 hours ago by rgl7194
Fuller Picture Emerges of Viral Video of Native American Man and Catholic Students - The New York Times
A fuller and more complicated picture emerged on Sunday of the videotaped encounter between a Native American man and a throng of high school boys wearing “Make America Great Again” gear outside the Lincoln Memorial in Washington.
Interviews and additional video footage suggest that an explosive convergence of race, religion and ideological beliefs — against a national backdrop of political tension — set the stage for the viral moment. Early video excerpts from the encounter obscured the larger context, inflaming outrage.
Leading up to the encounter on Friday, a rally for Native Americans and other Indigenous people was wrapping up. Dozens of students from Covington Catholic High School in Kentucky, who had been in Washington for the anti-abortion March for Life rally, were standing on the steps of the Lincoln Memorial, many of them white and wearing apparel bearing the slogan of President Trump.
There were also black men who identified themselves as Hebrew Israelites, preaching their beliefs and shouting racially combative comments at the Native Americans and the students, according to witnesses and video on social media.
news  politics  protest  racism  social_media  teenager  video  nytimes 
13 hours ago by rgl7194

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