Original: | worldwide because the author died at least 100 years ago. Public domainfalsefalse |
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Translation: | in the because it was published before January 1, 1929. in countries and areas where the copyright term is the author's . This work may be in the in countries and areas with longer native copyright terms that apply the to . Public domainfalsefalse |
January 12, 2024
Philipp Ammon for Quanta Magazine
Sarah Hart has always had an eye for the covert ways mathematics permeates other fields. As a child, she was struck by the ubiquity of the number 3 in her fairy tales. Hart’s mother, a math teacher, encouraged her pattern-seeking, giving her math puzzles to pass the time.
Hart went on to earn a doctorate in group theory in 2000 and later became a professor at Birkbeck, University of London. Hart’s research probed the structure of Coxeter groups, more general versions of structures that catalog the symmetries of polygons and prisms. In 2023, she published Once Upon a Prime , a book about the ways math appears in fiction and poetry. “Since we humans are part of the universe, it is only natural that our forms of creative expression, literature among them, will also manifest an inclination for pattern and structure,” Hart wrote. “Mathematics, then, is the key to an entirely different perspective on literature.”
Since 2020, Hart has been the professor of geometry at Gresham College in London. Gresham has no traditional courses; instead, its professors each deliver several public lectures per year. Hart is the first woman to ever hold the 428-year-old position, which was occupied in the 17th century by Isaac Barrow, famous for teaching another Isaac (Newton). More recently, it was held by Roger Penrose, a mathematician who won the 2020 Nobel Prize in Physics. Hart spoke with Quanta about how mathematics and art influence one another. The interview has been condensed and edited for clarity.
These links are less explored and less known than those between math and, say, music. The connections between mathematics and music have been celebrated since at least as far back as the Pythagoreans. However, though there has been writing and academic research about specific books, authors or genres, I hadn’t seen a book for a general audience about the broader connections between mathematics and literature.
Video : Sarah Hart, the professor of geometry at Gresham College, sees symmetry everywhere.
Video: Christopher Webb Young and Emily Buder/ Quanta Magazine ; Photo: Philipp Ammon for Quanta Magazine
There’s a lot of common ground between mathematics and, shall I say, the other arts. In literature, as well as music and art, you don’t ever start with nothing at all. If you’re a poet, you are choosing: Will I have a haiku with its very precise numerical constraints, or will I write a sonnet which has a certain number of lines, a certain rhyme scheme, a certain meter? Even something that doesn’t have a rhyme scheme will have line breaks, a rhythm. There will be constraints that inspire creativity, that help to focus you.
In mathematics, we have the same thing. We have some ground rules. Within that, we can explore, we can play, and we can prove theorems. What mathematics can do for the arts is help find new structures, show what the possibilities are. What would a piece of music look like that doesn’t have a key signature? We can think about the 12 tones and arranging them differently, and here are all the ways you can do that. Here are different color schemes you can devise, here are different forms of poetic meter.
Thousands of years ago in India, poets were trying to think about the possible meters. In Sanskrit poetry, you have long and short syllables. Long is twice as long as short. If you want to work out how many there are that take a length of time of three, you can have short, short, short, or long, short, or short, long. There are three ways to make three. There are five ways to make a length-four phrase. And there are eight ways to make a length-five phrase. This sequence you’re getting is one where every term is the sum of the previous two. You exactly reproduce what we nowadays call the Fibonacci sequence. But this was centuries before Fibonacci.
Hart is interested in the mathematical language found on this Babylonian cuneiform tablet, one of the earliest records of humans doing math.
A quite simple sequence, but it works very, very powerfully, is Eleanor Catton’s book The Luminaries , which came out in 2013. She used the sequence that goes 1,1/2, 1/4, 1/8, 1/16. Every chapter in that book is half the length of the one before. It creates this really fascinating effect, because the pace is picking up, and the characters’ choices are being more constrained. Everything hurtles toward its conclusion. By the end, the chapters are extremely short.
Another example of a slightly more complicated mathematical structure is what’s called orthogonal Latin squares. A Latin square is kind of like a sudoku grid. In this case, it’d be a 10-by-10 grid. Every number appears exactly once in each row and in each column. Orthogonal Latin squares are formed by overlaying two Latin squares so there is a pair of numbers in each space. The grid formed by the first number in each pair is a Latin square, and so is the grid formed by the second number in each pair. Furthermore, in the grid of pairs, no pair appears more than once.
These are very useful in all sorts of ways. You can make error-correcting codes out of them, which are useful for sending messages along kind of noisy channels. But one of the great things about these particular ones, size 10, is that one of the greatest mathematicians of all time, Leonhard Euler, thought they couldn’t exist. It was one of the very few times when he made a mistake; that’s why it was so exciting. A long time after he made this conjecture that these things couldn’t exist for particular sizes, it was refuted, and squares of this size were found in 1959. It was on the cover of Scientific American that year.
Hart has been making mathematical patterns since she was a young child.
Years after that, a French writer, Georges Perec, was looking for a structure to use for his book Life: A User’s Manual . He chose one of these orthogonal Latin squares. He set his book in a Paris apartment block, which had 100 rooms, a 10-by-10 square. Every chapter was in a different room, and every chapter had its unique flavor. He had lists of 10 things — various fabrics, colors, that kind of thing. Every chapter would use a unique combination. It’s a really fascinating way to structure the book.
It’s very variable! I know we prize brevity, but I think sometimes that is taken too far. There are too many papers that don’t have any useful examples.
What we actually prize is an ingenious argument that, because it covers all the cases at once so cleverly, is also brief and elegant. That is not the same as squashing your long argument into a smaller space than it needs by covering the page with arcane sigils that you’ve created to make the notation briefer, but which not only the reader but probably you yourself will have to unpack laboriously again in order to make any sense of what’s going on.
We don’t give enough thought to helpful notation which reminds the reader what is meant. The right notation can absolutely transform a piece of mathematics, and can make space for generalizations as well. Think of the transition, historically, from writing an unknown, its square and its cube with three different letters, and how much more likely, and even possible, it is to start thinking about when you have started writing , and instead.
Hart works from her home office, which sits in her back garden.
There are new things all the time. Fractals were everywhere in the 1990s. On every student dorm room wall, there was a picture of the Mandelbrot set or something like this. Everyone was like, “Oh, this is exciting, fractals.” You get, for example, musicians, composers, who are using fractal sequences in their compositions.
When I was about 16, there were these new things called graphics calculators. Very exciting. And a friend of my mother’s gave me this program that could draw a Mandelbrot set on one of these little graphics calculators. It had about, I don’t know, 200 pixels. You program this thing in, and then I had to leave it for 12 hours. It would plot these 200 points at the end of it. So even mere schoolchildren could engage with this in the late ’80s and early ’90s, and produce these pictures for themselves.
I think I’ve been interested since before I even knew that meant I was mathematical. Like, I just always was making patterns from when I was a tiny, weeny child.
When I was quite little, my favorite toy was some very simple wooden painted tiles. They came in all different colors. I would make them into patterns, and then I’d look at it proudly for a day or so, and then I’d make another one.
Hart with her bird, Coco, at her home in northeast London.
When I got a bit older, I would play with numbers and look at patterns. Mum would be the one I would go to and say, “I’m bored.” And then she’d say, “Well, can you work out what the pattern is of the number of points you need to make a triangle?” or whatever it was. She’d have me rediscover the triangular numbers or something, and I’d be very excited.
My poor mother, the number of amazing inventions that I would go to my mother with. “I’ve developed a whole new way of doing something!” And she’d say, “OK, that’s very nice. But, you know, Descartes thought of that centuries ago.” And then off I’d go; I’d come up with another amazing idea a few days later. “That’s lovely, dear. But the ancient Greeks had that one.”
The moments when you finally understand what the pattern is that you are seeing is always satisfying, as well as when you work out how to complete a proof you’ve been wrestling with. My strongest memories of those feelings of delight, probably because they were the first times I’d felt them, are from the start of my research career. But it’s still a lovely feeling to get that “aha,” when you finally understand what’s going on.
Very early on I was trying to prove something about infinite Coxeter groups. I’d resolved some of the cases, and in looking at the rest I came up with a technique that would work if a specific criterion was satisfied. You can write these relationships in a graph, so I started putting together a collection of the graphs for which my technique could be applied. This was over Christmas one year.
“Doing mathematics feels like discovery,” Hart said. “If we were inventing the mathematics, it surely wouldn’t be so hard to prove things! Sometimes we desperately want something to be true, and it isn’t.”
After a while, my set of pictures started to look like a particular set of graphs that were listed in a book about Coxeter groups that was in my office, and I began to hope that it was this exact set of graphs. If it was, then that would fill in the hole in my proof, and my theorem would be finished. But I couldn’t check for sure until I got back into the university after Christmas — this was before you could just Google everything. I think the anticipation of having to wait to confirm my hunch made it even better when I got to the book and compared my handwritten set of diagrams with the ones in the book, and they were indeed a match.
It probably is, though there are still some resonances.
Doing mathematics feels like discovery. If we were inventing the mathematics, it surely wouldn’t be so hard to prove things! Sometimes we desperately want something to be true, and it isn’t. We can’t avoid the consequences of logic, I suppose.
It all feels like discovery when you are doing it. Some choices mirror what we experience in the real world, like the axioms of geometry we work with, which are chosen because that seems to be roughly what reality is like — though even there, there’s no such thing as a “point” or a “line” (because we can’t draw something that takes up no space, and a line in geometry has no breadth and extends infinitely far).
To some extent, there are parallels to this continuum in literature. Once you define the rules of a sonnet, you will be hard-pressed to write one whose first line ends with “orange” or “chimney.”
But I can’t resist sharing something J.R.R. Tolkien said about writing The Hobbit : “It all began when I was reading exam papers to earn a bit of extra money. … Well, one day I came to a blank page in an exam book and I scribbled on it. ‘In a hole in the ground there lived a hobbit.’ I knew no more about the creatures than that, and it was years before his story grew. I don’t know where the word came from.”
Hobbits — did he create them or discover them?
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If you grew up in the '90s and aughts, these books—rapt with butterfly clips, cds, and myspace nostalgia—are for you.
You may or may not realize it, but the 1990s weren’t just a few years ago, not even just twenty years ago. Though the style has been resurrected of late by younger generations eager to grift the gritty grunge and combat boots of the final decade of the 20th century, and the same slip dresses and crop tops I wore in my high school years are all the rage on, we are now thirty years removed from 1995. Soak that in for a quick second if you will. The number of years millennials are from our most formative years are numbered enough to have earned a safe driver’s discount.
For those of you as stricken by me by the very thought, take consolation in the fact that we aren’t alone—there are others, especially elder millennials and late Generation Xers breaching the over 40 threshold, who are weeping alongside us—creaky knees, backaches, colonoscopy appointments and all. Rife with so much yesteryear reminiscence that you’ll be back to wearing low-rise jeans, butterfly clips, and burning CDs using pirated music sites in no time, my debut memoir collection, A Product of Genetics (and Day Drinking) , is guaranteed to send you straight into a memory spiral. If you ever bought a box of cereal based solely on the prize promised inside, yearned to be a Full House sibling, or explored hundreds of miles on a bike barefoot and unsupervised, this collection of essays is right up your alley.
The books below are a compilation of funny essay collections written by millennial women that will have you laughing and soaking in the nostalgia of days gone by. The authors of these books have voices that show that quirk is in and that stumbling on the way is the norm. These are the titles you might not have known that you needed (but most certainly do).
For anyone who wants to relive the horror of a Furby come alive in a darkened room (you do, I promise), this taste of growing up in the 1990s is the perfect dip into shared memories and the author’s tales of surviving being messy and trying to figure out who she is. In this fantastic collection of stories, readers can expect to laugh, cry, and commiserate—sometimes all at once.
If you aren’t already in love with this author, prepare yourself because you’re about to be all in. In this 2020 tome, West examines all our favorite movies with her inane ability to tell it like it is. Amusingly enough, West says all the things we’ve all been thinking for years, but in a better, funnier, more biting way that makes us wish we had actually said it first. In her examination of the hallmarks of cinema, she begs us to ask ourselves: Do these box office hits and cult classics still hold water? Did they deserve the hype in the first place? What in the actual hell? And should we be proud to admit that they’re our favorites or watch them in absolute zipper-mouth private never to be spoken of?
If there’s anyone who gets what it’s like to just not get it, it’s Sophia Benoit as described in this book of funny essays. Plan to laugh, cry, and feel confused, certain, uncertain, and wholly understood by the book’s end. This collection is such a chef’s kiss embodiment of what growing up in the 1990s was like for so many of our generation. It rides the waves of crappy dates, guilty pleasures, so much self-doubt that our brains runneth over, and a human experience so comfortingly familiar that you suspect that you and the author are meant to be forever besties.
More than anything, this one made me feel seen and realize that not feeling normal, not always understanding myself, not knowing how to human is, in fact, standard. The author celebrates the fact that from the beginning we are all just a bunch of mostly aimless weirdos. We start out weird and just eventually evolve and age into a different kind of weird. If you don’t get some comfort from that, we are not the same kind of person.
There’s a reason that this book was an instant New York Times Bestseller, it deserved to be. Dripping with all things deliciously pop culture and growing up as a millennial, Kennedy takes her essay collection to a new level with her hilarious take on being a woman, her lived experiences, and what our culture and time in space means. Each story in the book drives you to want more and read onward just to revel in the fact that it’s so damned nice to commiserate with someone who is still very much in their figuring-it-out era.
Experiences so awkward that just peeking into them is a bit mortifying, hot takes that make you feel like all that crap swirling around in your head isn’t as crazy as you suspect, and chapter after chapter with Irby’s trademark wit and humor go a long way in this recent release. If any book of hers will snag new readers, this is it. She talks about her love for Dave Matthews, run-ins with anaphylaxis, and moments of bare-bones honesty that sometimes just hit you in the face.
In this 2021 collection by the iconic comedian who is truly making things happen on and off the page, Robinson’s conversational tone and nothing-off-limits banter make you feel like you’re riding shotgun in your bestie’s car on the way to the store to buy the makings for margaritas. Whether she’s bemoaning the woes of dating or shelling out advice like a big sister, she keeps her essays funny, light, and pop culture-infused enough to always make a reader flip forward for just one more story before moving on.
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I see the ghost of myself sitting in a chair in the back of the classroom
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I began the pitch for “Fellow Travelers,” my adaptation of Thomas Mallon’s beautiful novel, with a piece of personal history. Growing up in a small Pennsylvania town in the 1960s, I never heard the word “homosexual” spoken aloud. There were no gay characters in movies, books or on television. I grew up believing that my hidden self was evil. Unspeakable.
I was captivated by Mallon’s story of Hawkins (Hawk) Fuller and Timothy Laughlin, two vastly different men conducting a passionate affair in 1950s Washington, D.C., during the government’s crusade against homosexuals. Hawk is selfish and confident. Tim is religious and sensitive. They struggle to love while hiding the part of themselves that allows them to love.
I was advised this story would be impossible to sell for three reasons: It was period, political and gay.
Being rebellious by nature, I decided to lean into the elements of the story that were deemed challenging. A period piece is problematic? In our scripts, every detail will be meticulously researched and much of the dialogue will come from historical records.
‘We were given the gift of a dream cast for a half-hour television comedy with mysterious twists and turns,’ writes ‘Only Murders’ showrunner John Hoffman. ‘We decided to triple down on the shot we were given.’
June 5, 2024
Rather than avoid politics, we’ll turn our political characters into flesh-and-blood antagonists, illuminating the dark secrets behind their destructive deeds. The whole thing is just too gay? We’ll create a gay love story with sex scenes that are passionate, tense and rough. We’ll take you on a gay sex tour through the decades, from park restrooms to backroom bars. In the end, we’ll break your heart.
We sold the show and made it. I have to acknowledge the executives at Fremantle and Showtime who embraced our “balls-out” approach (the expression seems apt) and my intrepid executive producers: Robbie Rogers, Dan Minahan and Matt Bomer.
We knew we needed to wrap our challenging elements inside a story that is universal and modern. The paranoia of the McCarthy era felt remote, and Mallon’s book ends in 1957. But I’d lived through the early days of AIDS, known the terror as those around me fell ill and died, and witnessed the hatred directed at my community.
I realized the AIDS crisis could serve as a bookend to the Lavender Scare. Tim would live in San Francisco, an activist, in the early days of the epidemic. Hawk will travel to Tim, seeking forgiveness, giving Tim power over Hawk in a reversal of their former roles. And these timelines will alternate throughout the show.
But the wheels of my mind kept turning. How might I bring Hawk and Tim together one or two more times? Again, I turned to personal history.
In high school, I was known as the sissy kid with liberal politics who loved Jesus. I protested the Vietnam War and refused to say the Pledge of Allegiance because the United States hadn’t yet achieved “liberty and justice for all.” When I was banished to the last row of desks in my homeroom, I considered it a badge of honor.
The sixth episode of the series, “Beyond Measure,” is set in 1968. Tim’s passionate anticommunist politics have morphed into antiwar politics. His Christianity, like mine in my youth, addresses his need to be exalted, to live and love “beyond measure.” In my teen years, my religious fervor offered what my peers found in sex, drugs and rock ’n’ roll.
I came out in the late 1970s, drinking, snorting and tumbling into bed with sweaty strangers after nights of dancing to Donna, Thelma and Grace. It was glorious. We had a few gay heroes but none more inspiring than Harvey Milk, the first nationally prominent gay politician. His murder was a shock and a wake-up call, reminding us that we’d only begun to win our freedom.
The Jewish stand-up comedian worked his interactions with white nationalists into “Just for Us,” an act that found its way to HBO.
May 29, 2024
Episode 7 of “Fellow Travelers,” “White Nights,” is set in 1979. Hawk and Tim reunite on Fire Island. They splash in the ocean, visit the “meat rack” and sweat on the dance floor. They seem free, until Hawk is forced to face excruciating grief. We placed our second set of lovers, Marcus and Frankie, in San Francisco, for the “explosion of gay rage” that followed the trial of Harvey Milk’s murderer, Dan White, and its obscene, lenient sentence.
Hawk’s grief, and his yearning to lose himself in drugs and sex, was informed by my own descent into alcoholism and addiction. The candlelight march honoring Milk that ends the episode is coupled with Hawk’s decision to return home. Twenty-five years ago, I began my own way home, finding a sober way to live.
The series ends at the National Mall in 1987 with the first display of the AIDS Quilt. Hawk kneels at Tim’s quilt square and gives words to the truth he’s carried in his heart for 3½ decades: “He was the man I loved.” Hawk finds redemption in speaking the unspeakable.
I know how he feels.
June 14, 2024
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Dr. Vivek Murthy said he would urge Congress to require a warning that social media use can harm teenagers’ mental health.
By Ellen Barry and Cecilia Kang
The U.S. surgeon general, Dr. Vivek Murthy, announced on Monday that he would push for a warning label on social media platforms advising parents that using the platforms might damage adolescents’ mental health.
Warning labels — like those that appear on tobacco and alcohol products — are one of the most powerful tools available to the nation’s top health official, but Dr. Murthy cannot unilaterally require them; the action requires approval by Congress.
The proposal builds on several years of escalating warnings from the surgeon general. In a May 2023 advisory, he recommended that parents immediately set limits on phone use, and urged Congress to swiftly develop health and safety standards for technology platforms.
He also called on tech companies to make changes: to share internal data on the health impact of their products; to allow independent safety audits; and restrict features like push notifications, autoplay and infinite scroll, which he says “prey on developing brains and contribute to excessive use.”
In an interview, Dr. Murthy said he had been deeply frustrated by the platforms’ reluctance to do so.
“I don’t think we can solely rely on the hope that the platforms can fix this problem on their own,” he said. “They’ve had 20 years.”
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921 Words4 Pages. INTRODUCTION Literature, in its wide range of sense, it is a written work of any single body. Literature is writing that is considered to be an art form. It is used to refer to all written account, though living at or belonging to the same time definitions extend the term to include text that are spoken or sung.
Through each era of American history, well-known figures in areas such as politics, literature, the arts, business, etc., voiced their opinions through short and long essays. Example 2 The ultimate persuasive essay that most students learn about and read in social studies is the "Declaration of Independence" by Thomas Jefferson in 1776.
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Introduction. Sarah Hart has always had an eye for the covert ways mathematics permeates other fields. As a child, she was struck by the ubiquity of the number 3 in her fairy tales. Hart's mother, a math teacher, encouraged her pattern-seeking, giving her math puzzles to pass the time. Hart went on to earn a doctorate in group theory in 2000 ...
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