The Mathematics Behind Origami, the Ancient Japanese Art of Paper Folding

The two characters at the core of origami (折り紙), one of the best-known Japanese words around the world, mean “folding” and “paper.” You might well have guessed that, but given the variety and elaborateness of the constructions produced by origami masters over the past few centuries, the simplicity of the practice’s basic nature bears repeating. Those masters must develop no slight degree of manual dexterity, it goes without saying, but also a formidable mathematical understanding of their medium. In many cases that understanding is intuitive; in the TED-Ed lesson above, origami artist Evan Zodl makes it explicit.

Zodl’s lesson explains that “though most origami models are three-dimensional, their crease patterns are usually designed to fold flat, without introducing any new creases or cutting the paper.”(Incidentally, the Japanese word for paper art involving cuts is kirigami, or 切り紙.)




An “abstract, 2D design” thus becomes, in the origami master’s hands, “a 3D form,” but only in accordance with a set of four simple rules Zodl explains. He does so clearly and understandably — and in a way that for many of us may exhume buried geometry-class memories — but like actual works of origami, they’re better shown than described: hence the vivid accompanying animations of Charlotte Arene.

Origami’s principles and products may be fascinating to contemplate, but “the ability to fold a large surface into a compact shape” has also proven to have serious real-world applications. Zodl points to an origami-based re-imagination of “the traditional stent graft, a tube used to open and support damaged blood vessels.” This in addition to “airbags, solar arrays, self-folding robots, and even DNA nanostructures” — as well as a massive “star shade” for space telescopes that blocks the glare of nearby stars. If you’d like to get started on your own tactile understanding of all this, do have a look at Zodl’s own Youtube channel, as well as others like Origami Instructions. Don’t let the elaborately folded flowers, boats, or animals you’ve seen intimidate you; start with a simple box and work your way up from there. If origami shows us anything, after all, it’s that complexity begins with simplicity.

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

A Search Engine for Finding Free, Public Domain Images from World-Class Museums

Even before the pandemic, museums were putting their art online. Here on Open Culture, we’ve covered such ambitious efforts of digitization and making-available on the part of the Rijksmuseum, the Art Institute of Chicago, and other major institutions, some of whom have gone so far as to upload their holdings under Creative Commons licenses or in other free-to-use forms. And now you can call forth artworks from the open online collections and others all at once with the search engine Museo.

Museo is a visual search engine that connects you with the Art Institute of Chicago, the Rijksmuseum, the Minneapolis Institute of Art and the New York Public Library Digital Collection,” writes creator Chase McCoy, who also emphasizes that connections with more such collections are to come.




“Every image you find here is in the public domain and completely free to use, although crediting the source institution is recommended!”

Imagine you need images to illustrate an essay about, say, travel. Punch that word into Museo (or a related one like “journey”) and out come a variety of paintings, prints, drawings, sculptures, books, maps, housewares, and other items found in museums. Here we have Adolph Menzel’s In a Railway Carriage (After a Night’s Journey) from 1851, Katsushika Hokusai’s The Eastern Journey of the Celebrated Poet Ariwara no Narihira from 1806, Aelbert Cuyp’s River Landscape with Riders from the mid-1650s, Seth Eastman’s Indians Travelling from 1850, and Richard Newton’s On a Journey to a Courtship in Wales from 1795.

The results are hardly limited to conventional works like these: you’ll also find such curiosities as an early 19th-century traveling desk; a portable bank from 1904 called the “traveling teller”; a 1920 image “showing the earth bisected centrally through the polar openings and at right angles to the equator, giving a clear view of the central sun and the interior continents and oceans”; Henry Corry Rowley Becher’s 1880 travelogue A Trip to Mexico; and the Automobile Club of Hartford’s 1922 Motor Trips guide to New England and eastern New York.

Most of the art available through Museo comes, as public-domain material tends to, from times long past. But that, in its own way, encourages their creative use: many of the images returned for “entertainment,” “food,” “sports,” and even “technology” fairly demand surprising 21st-century recontextualization. As its network of collections expands, do make a point of visiting Museo every so often to search for your own subjects of interest; your next big idea may well be inspired by art from a century or two (or three, or four) ago.

via Austin Kleon

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

The Letters of Mozart’s Sister Maria Anna Get Transformed into Music

The talent of an individual may not always run in the family, but we can never discount the possibility of its doing so. This is true even in the case of Wolfgang Amadeus Mozart, not just one of the best-known composers ever to live, but a byword for deep, innate, and unrepeatable genius. Mozart was composing original music at the age of of four or five, an astonishing fact we know today in part because his older sister witnessed and later attested to it. Known as Nannerl, Maria Anna Mozart preceded her bother into keyboard lessons from their father Leopold, a composer and teacher. Together Wolfgang and Maria Anna toured Europe as a performing duo of child prodigies, until Maria Anna’s attainment of marriageable age took her off the circuit.

If Maria Anna ever composed music of her own, none of it has survived. But she did leave behind a fair few diaries and letters, many of the latter exchanged with her brother. These writings provided the material for pianist Heloísa Fernandes to create a piece in tribute to the lesser-known Mozart sibling.




“The writing, all in German, underwent painstaking analysis so that its tone and pronunciation could be translated into musical notes,” says Little Black Book. “A German interpreter was invited to read the letters and diary of Maria Anna Mozart out loud,” and a piece of software “translated the recording into musical notes by tuning the syllables. If a spoken syllable hit 387 Hz, for example, the program interpreted it as G.” Thus were Nannerl’s words transformed into music.

The resulting piece, “Das Königreich Rücken,” is named after “an imaginary kingdom that Maria and Wolfgang made reference to in their letters to each other,” as Sara Spary notes in Adweek — a publication that would naturally cover it, commissioned as it was by an ad campaign for LG Electronics. Developed by Brazilian firm AlmapBBDO in cooperation with the production company Supersônica, “Projecto Ms. Mozart” is meant to promote LG’s XBOOM Go Bluetooth speaker. But whichever device you use to hear “Das Königreich Rücken,” you’ll surely find that it sounds quite unlike any piece you’ve heard before. Fans of Maria Anna Mozart as a historical figure will listen and wonder what could have been, and even those ignorant of her can’t but welcome these three additional minutes of Mozart into the world.

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

The Iconic Dance Scene from Hellzapoppin’ Presented in Living Color with Artificial Intelligence (1941)

After Charles Lindbergh “hopped” the Atlantic in 1927, his history-making solo flight set off a craze for all things “Lindy.” Of the countless songs, foods, products, and trends created or named in honor of the famous onetime U.S. Air Mail pilot, only one remains recognizable these more than 90 years later: the Lindy Hop. Developed on the streets and in the clubs of Harlem, the dance proved explosively popular, though it took Hollywood a few years to capitalize on it. In the late 1930s, the musical Hellzapoppin’ brought the Lindy Hop to Broadway, and in 1941, Universal Pictures turned that stage show into a major motion picture directed by H.C. Potter (now best known for Mr. Blandings Builds His Dream House).

An often surreal, fourth-wall-breaking affair, Hellzapoppin’ is remembered mainly for the five-minute Lindy Hop musical number that comes about halfway through the film. It features a dance troupe called the Harlem Congaroos, played by the real-life Whitey’s Lindy Hoppers, a group of professional swing dancers founded at Harlem’s Savoy Ballroom, the origin point of the Lindy Hop as we know it today.




Its appearing members include Frankie Manning, whose name had become synonymous with the Lindy Hop in the 1930s, and Norma Miller, who as a twelve-year-old girl famously did the dance outside the Savoy for tips. Hellzapoppin’ preserves their athleticism and vitality for all time — with a hot jazz soundtrack to boot.

Like most Hollywood musicals of the early 1940s, Hellzapoppin’ was shot in black-and-white, and cinephiles will maintain that it’s best seen that way. But just as the technology powering long-haul flights has developed greatly since the days of Charles Lindbergh, so has the technology of film colorization. Take DeOldify, the “open-source, Deep Learning based project to colorize and restore old images and film footage” that “uses AI neural networks trained with thousands of reference pictures” – and that was used to produce the version of Hellzapoppin‘s Lindy Hop number seen at the top of the post. It all looks much more convincing than when Ted Turner attempted to colorize Citizen Kane, but in lovers of dance, whatever sense of realism DeOldify contributes will mainly inspire a deeper longing to experience the culture of Harlem as it really was in the 1920s.

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

Flim: a New AI-Powered Movie-Screenshot Search Engine

There was a time when cinephile shorthand consisted mostly of quotations from movies — from movies’ dialogue, to be precise. The distinction matters these days, now that the internet has enabled us to communicate just as easily with visual quotations as verbal ones. While some of us go the extra mile by manually combing through our film collections and taking the screenshots that best reflect our personal sentiments, most of us have long relied on the results, however approximate, served up by search engines like Google Images.

Now a promising new solution has emerged, called Flim (not to be confused with “film”). Described on its about page as “a constantly evolving database of HD screenshots,” with a claim of 50,000 provided daily, Flim uses artificial intelligence to perform color analysis and detect “objects, clothes, characters, etc.”




This means that when you enter terms like “tree,” “guitar,” “tuxedo,” or “pizza,” you get a selection of images including trees, guitars, tuxedos, and pizzas, all taken straight from a range of motion pictures wide enough to include The Nightmare Before Christmas and An American Werewolf in LondonEasy Rider and Wayne’s World 2, Mélo and Wedding Crashers.

Artificial intelligence has come a long way in recent years, especially in its capacity to recognize the content of images. The one driving Flim does seem to have committed the occasional amusing misfile, but it’s still early days. And though cinephiles will be quick to notice the omissions in its database, they’ll find a great deal of visual material from the work of their favorite auteurs: more than 100 screenshots from that of David Lynch, more than 300 from that of Éric Rohmer, more than a thousand from that of Stanley Kubrick, and nearly 1,500 from that of Alfred Hitchcock.

“I would love for the screenshot detail pages to include timecodes,” suggests Jason Kottke. It would make this an amazing tool for creating supercuts, film analysis videos, and other sorts of media. Imagine how much easier Christian Marclay’s job would have been with ‘clock’ and ‘watch’ searches on Flim.” Certainly I could have used it while making my own video essay on Los Angeles’ Bonaventure Hotel, a notable film-shoot location over the past few decades — though as yet the Bonaventure’s name returns no results, nor do the names of any other real-world buildings that come to mind.

Still, if Flim expands apace, it will become a valuable resource for cinephiles and non-cinephiles alike, as well as filmmakers themselves: No Film School’s Jason Hellerman describes it as a potentially revolutionary aid for the assembly of “mood boards” and “lookbooks,” industry-standard elements of pitch presentations for “music videos, features, and commercials.” As with any newly developed tool of this kind, though, the most interesting uses will surely be the least obvious ones. In time, Flim could even prove to be a trusted source of reading recommendations.

via Kottke

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

Wired Co-Founder Kevin Kelly Gives 36 Lectures on Our Future World: Education, Movies, Robots, Autonomous Cars & More

Given recent events, 2019 may now seem to us like the distant past. But to those who were thinking hard about the future the year before last, nothing that has happened since has been wholly unexpected — and especially not to those who’d already been thinking hard about the future for decades. Take Kevin Kelly, co-founder of Wired magazine and writer on technology as well as a host of other subjects. It was in 2019 that state telecommunications company China Mobile commissioned him to give a series of 36 short video lectures on the “Future of X”: not the future of the internet in China and the future of India in competition with China, but a range of topics that will surely affect us all, no matter our part of the world.

Self-driving cars, virtual reality, 5G, robots: Kelly has given consideration to all these much-discussed technologies and the roles they may come to play in our lives. But the important thing about them isn’t to know what form they’ll take in the future, since by definition no one can, but to develop habits of mind that allow you to grasp as wide a variety of their possibilities as you can right now.




The future, as Kelly frames it in his talk on uncertainties, consists of “known knowns,” “known unknowns,” and “unknown unknowns.” Those last, better known as “black swans,” are events “completely unexpected by anybody” that “change the world forever.” As examples of possible black swans to come he names World War Three, the discovery of cheap fusion energy, and, yes, a pandemic.

Societal preparation for the future, to Kelly’s mind, will involve developing “a very systematic way of collecting these unknown unknowns and turning them into known unknowns.” Personal preparation for the future, according to his talk on schools and learning, will involve ceaseless acquisition and refinement of knowledge and understanding.

If we want to thrive in an uncertain future, he argues, we should “adopt a method of learning called deliberate practice, falling forward or failing forward,” in which we keep pushing ourselves into unknown intellectual territory, always remaining “newbies” at something, assisted all the while by technology.

Just a couple of decades into the 21st century, we’ve already caught a glimpse of what technology can do to optimize our learning process — or simply to enable learning where it wouldn’t happen otherwise. “I don’t imagine that we’re going to go away from a classroom,” Kelly says, but we also “have the online video world, and more and more people today are learning how to do an amazing variety of things, that we wouldn’t have thought would work on video.”

Of course, since he spoke those words, one black swan in particular has pushed much of humanity away from the classroom, and we’ve found out a good deal more about what kind of learning works (and doesn’t) over the internet. The future, it seems, is now.

You can watch the full playlist of videos, all 36 of them, below. We also recommend his very insightful book, The Inevitable: Understanding the 12 Technological Forces That Will Shape Our Future.

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

Why Public Transit Sucks in the United States: Four Videos Tell the Story

Many different words could describe the state of public transportation in America today. In recent decades, more and more of a consensus seems to have settled around one word in particular: that it “sucks.” Given its “antiquated technology, safety concerns, crumbling infrastructure,” and often “nonexistence,” says the narrator of the video above, “it’s not hard to argue that the U.S. public transportation network is just not good.” That narrator, Sam Denby, is the creator of Wendover Productions, a Youtube channel all about geography, technology, economics, and the infrastructure where all three intersect. He believes not only that America’s public transit sucks, but that the country’s “lack of solid public transportation almost defines American culture.”

This would make a certain sense in a poor, small, struggling country — but not in the United States of America, described not long ago by Anne Applebaum in the Atlantic as “accustomed to thinking of itself as the best, most efficient, and most technologically advanced society in the world.”




As anyone making their first visit will experience, America’s still-formidable wealth and power doesn’t square with the experience on the ground, or indeed under it: whether by subway, bus, or streetcar, the task of navigating most U.S. cities is characterized by inconvenience, discomfort, and even impossibility. This in a country whose public transportation once really was the envy of the world: at the turn of the 20th century, its cities boasted 11,000 miles of streetcar track alone.

In the mid-2010s, by Denby’s reckoning, “the combined mileage of every tram, subway, light rail, and commuter rail system” added up only to 5,416. What happened in the hundred or so years between? He cites among other factors the production of the first widely affordable automobiles in the 1920s, and later that of buses, with their lower operating costs than streetcars — but as commonly operated today, their lower-quality transit experience as well. (Resentment about this large-scale replacement of urban streetcar systems runs deep enough to make some consider it a conspiracy.) The U.S. “grew up as the car grew up, so its cities were built for cars,” especially in its more recently settled west. Indirect subsides lowered the cost of gas, and from the 1950s the building of the Interstate Highway System made it easy, at least for at time, to commute between city and suburb.

As pointed out in the Vox videos “Why American Public Transit Is So Bad” and “How Highways Wrecked American Cities,” these massive roads ran not around or under cities (as they do in much of Europe and Asia) but straight through their centers, part of a larger process of “urban renewal” that ironically destroyed quite a few of what dense urban neighborhoods the U.S. had. More than half a century of highway-building, suburbanization, and strict zoning later, most Americans find themselves unable to get where they need to go without buying a car and driving themselves. The situation is even worse for those traveling between cities, as examined above in Wendover Productions’ “Why Trains Suck in America.” As an American, I take a certain satisfaction in hearing these questions addressed — but I take an even greater one in being an American living abroad.

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

A 10 Billion Pixel Scan of Vermeer’s Masterpiece Girl with a Pearl Earring: Explore It Online

We admire Johannes Vermeer’s Girl with a Pearl Earring for many reasons, not least that it looks exactly like a girl with a pearl earring. Or at least it does from a distance, as the master of light himself no doubt stepped back to confirm countless times during the painting process, at any moment of which he would have been more concerned with the brushstrokes constituting only a small part of the image. But even Vermeer himself could have perceived only so much detail of the painting that would become his masterpiece.

Now, more than 350 years after its completion, we can get a closer view of Girl with a Pearl Earring than anyone has before through a newly released 10 billion-pixel panorama. At this resolution, writes Petapixel’s Jason Schneider, we can “see the painting down to the level of 4.4-microns per pixel.”




Undertaken by Emilien Leonhardt and Vincent Sabatier of 3D microscope maker Hirox Europe “in order to evaluate the surface condition of the painting, measure cracks, and see the topography of various key areas while assessing past restorations,” the project required taking 9,100 photos, which “were automatically captured and stitched together to form one finished panorama image where one pixel equals 4.4 microns.”

You’ll understand what this means if you view the panorama and click the plus symbol on the bottom control bar to zoom in — and click it again, and again, and again. (Or just click it and hold it down.) Before long, Girl with a Pearl Earring will look less like a girl with a pearl earring than what she really is: centuries-old oil paints on a centuries-old canvas. The physicality of this work of art, one so often held up as the realization of aesthetic ideal, becomes even less ignorable if you click the “3D” button. This presents ten individual sections of the painting scanned in three dimensions, which you can freely rotate and even light from all directions.

The 3D-scanned portions include the titular pearl earring, which appears to have a bit of a gouge in it. They’re more clearly visible in 5x topographical viewing mode (selectable on the top control bar). This official Hirox video offers a glimpse of the procedure required to achieve the kind of unprecedentedly high-resolution view of Girl with a Pearl Earring that allows us to behold details heretofore practically invisible. At more than 10,000 megapixels, the background reveals itself to be in fact a dark green curtain, and the girl herself has clearly defined eyelashes. But as for her long-speculated-about identity, well, there are some things microscopy can’t determine. Take a close look at Vermeer’s painting here. And if you’d like to take a similar look at Rembrandt’s The Night Watch, click here.

via Colossal

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletterBooks on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall, on Facebook, or on Instagram.

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