In 20th-century mathematics, the renowned name of Nicolas Bourbaki stands alone in its class — the class, that is, of renowned mathematical names that don’t actually belong to real people. Bourbaki refers not to a mathematician, but to mathematicians; a whole secret society of them, in fact, who made their name by collectively composing Elements of Mathematic. Not, mind you, Elements of Mathematics: “Bourbaki’s Elements of Mathematic — a series of textbooks and programmatic writings first appearing in 1939—pointedly omitted the ‘s’ from the end of ‘Mathematics,'” writes JSTOR Daily’s Michael Barany, “as a way of insisting on the fundamental unity and coherence of a dizzyingly variegated field.”
That’s merely the tip of Bourbaki’s iceberg of eccentricities. Formed in 1934 “by alumni of the École normale supérieure, a storied training ground for French academic and political elites,” this group of high-powered mathematical minds set about rectifying their country’s loss of nearly an entire generation of mathematicians in the First World War. (While Germany had kept its brightest students and scientists out of battle, the French commitment to égalité could permit no such favoritism.) It was the pressing need for revised and updated textbooks that spurred the members of Bourbaki to their collaboratively pseudonymous, individually anonymous work.
“Yet instead of writing textbooks,” explains Quanta‘s Kevin Hartnett, “they ended up creating something completely novel: free-standing books that explained advanced mathematics without reference to any outside sources.” The most distinctive feature of this already unusual project “was the writing style: rigorous, formal and stripped to the logical studs. The books spelled out mathematical theorems from the ground up without skipping any steps — exhibiting an unusual degree of thoroughness among mathematicians.” Not that Bourbaki lacked playfulness: “In fanciful and pun-filled narratives shared among one another and alluded to in outward-facing writing,” adds Barany, “Bourbaki’s collaborators embedded him in an elaborate mathematical-political universe filled with the abstruse terminology and concepts of modern theories.”
You can get an animated introduction to Bourbaki, which survives even today as a still-prestigious and at least nominally secret mathematical society, in the TED-Ed lesson above. In the decades after the group’s founding, writes lesson author Pratik Aghor, “Bourrbaki’s publications became standard references, and the group’s members took their prank as seriously as their work.” Their commitment to the front was total: “they sent telegrams in Bourbaki’s name, announced his daughter’s wedding, and publicly insulted anyone who doubted his existence. In 1968, when they could no longer maintain the ruse, the group ended their joke the only way they could: they printed Bourbaki’s obituary, complete with mathematical puns.” And if you laugh at the mathematical pun with which Aghor ends the lesson, you may carry a bit of Bourbaki’s spirit within yourself as well.
We tend to imagine Pompeii as a city frozen in time by the eruption of Mount Vesuvius, inhabitants and all, but most Pompeiians actually survived the disaster. “The volcano’s molten rock, scorching debris and poisonous gases killed nearly 2,000 people” in Pompeii and nearby Herculaneum, writes Live Science’s Laura Geggel. Of the 15,000 and 20,000 people in total who’d lived there, “most stayed along the southern Italian coast, resettling in the communities of Cumae, Naples, Ostia and Puteoli,” according to the latest archaeological research. Vesuvius may have made refugees of them, but history has revealed that they made the right choice.
Pompeiians in particular, as the TED-Ed lesson above depicts it, faced three choices: “seek shelter, escape to the south on foot, or flee to the west by sea,” the latter made a viable proposition by the town’s location near the coast. The video’s animation (scripted by archaeology Gary Devore) dramatizes the fates of three siblings, Lucius, Marcus, and Fabia, on that fateful day in A.D. 79. “Fabia and her brothers discuss the recent tremors everyone’s been feeling,” says the narrator. “Lucius jokes that there’ll always be work for men who rebuild walls in Pompeii.” It is then that the long-rumbling Vesuvius emits a “deafening boom,” then spews “smoke, ash, and rock high into the air.”
Gathering up his own family from Herculaneum, Marcus goes seaward, but the waves are “brimming with volcanic matter, making it impossible for boats to navigate close enough to shore.” As subsequent phases of the eruption further devastate the towns, the luckless Lucius finds himself entombed in the room where he’d been awaiting his fiancée. Sheltering with her husband and daughters, and hearing the roof of her home “groan under the weight of volcanic debris,” Fabia alone makes the choice to join the stream of humanity walking southeast, away from the volcano. This sounds reasonable, although when Wired‘s Cody Cassidy asks University of Naples Federico II forensic anthropologist Pier Paolo Petrone to recommend the best course of action, the expert suggests fleeing to the north, toward Herculaneum and finally Naples — and more immediately, toward Vesuvius.
“The road between Pompeii and Naples was well maintained,” Petrone tells Cassidy, “and the written records of those who survived suggest that most of the successful escapees went north — while most of the bodies of the attempted escapees (who admittedly left far too late) have been found to the south.” Should you find yourself walking the thirteen miles between between Pompeii and Naples in the midst of a volcanic eruption, you should “avoid overexertion and take any opportunity to drink fresh water.” As Petrone writes, “only those who managed to understand from the beginning the gravity of the situation” — the Fabias, in other words — “escaped in time.” The likes of Mount Vesuvius would seem to rank low on the list of dangers facing humanity today, but nearly two millennia after Pompeii, it is, after all, still active.
The conference took place 15 years after Henson’s untimely death, leaving Kermit to be animated by Steven Whitmire, the first of two puppeteers to tackle a role widely understood to be Henson’s alter ego.
The voice isn’t quite the same, but the mannerisms are, including the throat clearing and crumpled facial expressions.
Also present are a number of TED Talk tropes, the smart phone prompts, the dark stage, projections designed to emphasize profound points.
A number of jokes fail to elicit the expected laughs … we’ll leave it up to you to determine whether the fault lays with the live audience or the material. (It’s not easy being green and working blue comes with challenges, too.)
Were he to give his TED Talk now, in 2021, Kermit probably wouldn’t describe the audience’s collective decision to “accept a premise, suspend our disbelief and just enjoy the ride” as a “conspiracy of craziness.”
He might bypass a binary quote like “If necessity is the mother of invention, then creativity is the father.”
He’d also be advised to steer clear of a photo of Miss Piggy dressed as a geisha, and secure her consent to share some of the racier anecdotes… even though she is a known attention hog.
He would “transcend and include” in the words of philosopher Ken Wilber, one of many inspirations he cites over the course of his 23-minute consideration of creativity and its origins, attempting to answer the question, “Why are we here?”
Also referenced: Michelangelo, Albert Einstein, Salvador Dali, Charles Baudelaire, Zen master Shunryū Suzuki, mathematician Alfred North Whitehead, author and educator, Sir Ken Robinson (who appears, briefly) and of course, Henson, who applauded the “ridiculous optimism” of flinging oneself into creative explorations, unsure of what one might find.
He can’t wander freely about the stage, but he does share some stirring thoughts on collaboration, mentors, and the importance of maintaining “beginner’s mind,” free of pre-conceptions.
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.
Those in a position to know suggest that vermin shy away from yellowish-greens such as that favored by the Emperor because they “resemble areas of intense lighting.”
We’d like to offer an alternate theory.
Could it be that the critters’ ancestors passed down a cellular memory of the perils of arsenic?
Napoleon, like thousands of others, was smitten with a hue known as Scheele’s Green, named for Carl Wilhelm Scheele, the German-Swedish pharmaceutical chemist who discovered oxygen, chlorine, and unfortunately, a gorgeous, toxic green pigment that’s also a cupric hydrogen arsenite.
Scheele’s Green, aka Schloss Green, was cheap and easy to produce, and quickly replaced the less vivid copper carbonate based green dyes that had been in use prior to the mid 1770s.
The color was an immediate hit when it made its appearance, showing up in artificial flowers, candles, toys, fashionable ladies’ clothing, soap, beauty products, confections, and wallpaper.
A month before Napoleon died, he included the following phrase in his will: My death is premature. I have been assassinated by the English oligopoly and their hired murderer…”
His exit at 51 was indeed untimely, but perhaps the wallpaper, and not the English oligopoly, is the greater culprit, especially if it was hung with arsenic-laced paste, to further deter rats.
When Scheele’s Green wallpaper, like the striped pattern in Napoleon’s bathroom, became damp or moldy, the pigment in it metabolized, releasing poisonous arsenic-laden vapors.
Napoleon’s First Valet Louis-Joseph Marchand recalled the “childish joy” with which the emperor jumped into the tub where he relished soaking for long spells:
The bathtub was a tremendous oak chest lined with lead. It required an exceptional quantity of water, and one had to go a half mile away and transport it in a barrel.
In Napoleon’s case, arsenic was likely just one of many compounds taxing an already troubled system. In the course of treatments for a variety of symptoms—swollen legs, abdominal pain, jaundice, vomiting, weakness—Napoleon was subjected to a smorgasbord of other toxic substances. He was said to consume large amounts of a sweet apricot-based drink containing hydrocyanic acid. He had been given tarter emetic, an antimonal compound, by a Corsican doctor. (Like arsenic, antimony would also help explain the preserved state of his body at exhumation.) Two days before his death, his British doctors gave him a dose of calomel, or mercurous chloride, after which he collapsed into a stupor and never recovered.
As Napoleon was vomiting a blackish liquid and expiring, factory and garment workers who handled Scheele’s Green dye and its close cousin, Paris Green, were suffering untold mortifications of the flesh, from hideous lesions, ulcers and extreme gastric distress to heart disease and cancer.
Fashion-first women who spent the day corseted in voluminous green dresses were keeling over from skin-to-arsenic contact. Their seamstresses’ green fingers were in wretched condition.
In 2008, an Italian team tested strands of Napoleon’s hair from four points in his life—childhood, exile, his death, and the day thereafter. They determined that all the samples contained roughly 100 times the arsenic levels of contemporary people in a control group.
Napoleon’s son and wife, Empress Josephine, also had noticeably elevated arsenic levels.
Had we been alive and living in Europe back then, ours likely would have been too.
All that green!
But what about the wallpaper?
A scrap purportedly from the dining room, where Napoleon was relocated shortly before death, was found by a woman in Norfolk, England, pasted into a family scrapbook above the handwritten caption, This small piece of paper was taken off the wall of the room in which the spirit of Napoleon returned to God who gave it.
In 1980, she contacted chemist David Jones, whom she had recently heard on BBC Radio discussing vaporous biochemistry and Victorian wallpaper. She agreed to let him test the scrap using non-destructive x-ray fluorescence spectroscopy. The result?
.12 grams of arsenic per square meter. (Wallpapers containing 0.6 to 0.015 grams per square meter were determined to be hazardous.)
Dr. Jones described watching the arsenic levels peaking on the lab’s print out as “a crazy, wonderful moment.” He reiterated that the house in which Napoleon was imprisoned was “notoriously damp,” making it easy for a 19th century fan to peel off a souvenir in “an inspired act of vandalism.”
Death by wallpaper and other environmental factors is definitely less cloak and dagger than assassination by the English oligopoly, hired murderer, and other conspiracy theories that had thrived on the presence of arsenic in samples of Napoleon’s hair.
As Dr. Jones recalled:
…several historians were upset by my claim that it was all an accident of decor…Napoleon himself feared he was dying of stomach cancer, the disease which had killed his father; and indeed his autopsy revealed that his stomach was very damaged. It had at least one big ulcer…My feeling is that Napoleon would have died in any case. His arsenical wallpaper might merely have hastened the event by a day or so. Murder conspiracy theorists will have to find new evidence!
We can’t resist mentioning that when the emperor was exhumed and shipped back to France, 19 years after his death, his corpse showed little or no decomposition.
Green continues to be a noxious color when humans attempt to reproduce it in the physical realm. As Alice Rawthorn observed The New York Times:
The cruel truth is that most forms of the color green, the most powerful symbol of sustainable design, aren’t ecologically responsible, and can be damaging to the environment.
Ayun Halliday is an author, illustrator, theater maker and Chief Primatologist of the East Village Inky zine. She most recently appeared as a French Canadian bear who travels to New York City in search of food and meaning in Greg Kotis’ short film, L’Ourse. Follow her @AyunHalliday.
Is this what we want? A post-truth world where toxicity and tribalism trump bridge building and consensus seeking? —Yaël Eisenstat
It’s an increasingly familiar occurrence.
A friend you’ve enjoyed reconnecting with in the digital realm makes a dramatic announcement on their social media page. They’re deleting their Facebook account within the next 24 hours, so shoot them a PM with your email if you’d like to stay in touch.
Such decisions used to be spurred by the desire to get more done or return to neglected pastimes such as reading, painting, and going for long unconnected nature walks.
These announcements could induce equal parts guilt and anxiety in those of us who depend on social media to get the word out about our low-budget creative projects, though being prone to Internet addiction, we were nearly as likely to be the one making the announcement.
For many, the break was temporary. More of a social media fast, a chance to reevaluate, rest, recharge, and ultimately return.
Legitimate concerns were also raised with regard to privacy. Who’s on the receiving end of all the sensitive information we’re offering up? What are they doing with it? Is someone listening in?
But in this election year, the decision to quit Facebook is apt to be driven by the very real fear that democracy as we know it is at stake.
Eisenstat contrasts the civility of her past face-to-face ”hearts and minds”-based engagements with suspected terrorists and anti-Western clerics to the polarization and culture of hatred that Facebook’s algorithms foment.
As many users have come to suspect, Facebook rewards inflammatory content with amplification. Truth does not factor into the equation, nor does sincerity of message or messenger.
Lies are more engaging online than truth. As long as [social media] algorithms’ goals are to keep us engaged, they will feed us the poison that plays to our worst instincts and human weaknesses.
Eisenstat, who has valued the ease with which Facebook allows her to maintain relationships with far-flung friends, found herself effectively demoted on her second day at the social media giant, her title revised, and her access to high level meetings revoked. Her hiring appears to have been purely ornamental, a palliative ruse in response to mounting public concern.
They are making all sorts of reactive changes around the margins of the issues, [to suggest] that they are taking things seriously – such as building an ad library or verifying that political advertisers reside in the country in which they advertising – things they should have been doing already. But they were never going to make the fundamental changes that address the key systemic issues that make Facebook ripe for manipulation, viral misinformation and other ways that the platform can be used to affect democracy.
First of all, it’s another example of Facebook putting responsibility on someone else. The oversight board does not have any authority to actually address any of the policies that Facebook writes and enforces, or the underlying systemic issues that make the platform absolutely rife for disinformation and all sorts of bad behaviour and manipulation.
The second issue is: it’s basically an appeal process for content that was already taken down. The bigger question is the content that remains up. Third, they are not even going to be operational until late fall and, for a company that claims to move fast and break things, that’s absurd.
Nine minutes into her TED Talk, she offers concrete suggestions for things the Facebook brass could do if it was truly serious about implementing reform:
Stop amplifying and recommending disinformation and bias-based hatred, no matter who is behind it—from conspiracy theorists to our current president.
Discontinue personalization techniques that don’t differentiate between targeted political content and targeted ads for athletic footwear.
Retrain algorithms to focus on a metrics beyond what users click or linger on.
Implement safety features that would ensure that sensitive content is reviewed before it is allowed to go viral.
Hopefully viewers are not feeling maxed out on contacting their representatives, as government enforcement is Eisenstat’s only prescription for getting Facebook to alter its product and profit model. And that will require sustained civic engagement.
When next you meet an existentialist, ask him what kind of existentialist s/he is. There are at least as many varieties of existentialism as there have been high-profile thinkers propounding it. Several major strains ran through postwar France alone, most famously those championed by Jean-Paul Sartre, Simone de Beauvoir, and Albert Camus — who explicitly rejected existentialism, in part due to a philosophical split with Sartre, but who nevertheless gets categorized among the existentialists today. We could, perhaps, more accurately describe Camus as an absurdist, a thinker who starts with the inherent meaningless and futility of life and proceeds, not necessarily in an obvious direction, from there.
The animated TED-Ed lesson above sheds light on the historical events and personal experiences that brought Camus to this worldview. Beginning in the troubled colonial Algeria of the early 20th-century in which he was born and raised, educator Nina Medvinskaya goes on to tell of his periods as a resistance journalist in France and as a novelist, in which capacity he would write such enduring works as The Stranger and The Plague. Medvinskaya illuminates Camus’ central insight with a well-known image from his earlier essay “The Myth of Sisyphus,” on the Greek king condemned by the gods to roll a boulder up a hill for all eternity.
“Camus argues that all of humanity is in the same position,” says Medvinskaya, “and only when we accept the meaninglessness of our lives can we face the absurd with our heads held high.” But “Camus’ contemporaries weren’t so accepting of futility.” (Here the Quentin Blake-style illustrations portray a couple of figures bearing a strong resemblance to Sartre and de Beauvoir.) Many existentialists “advocated for violent revolution to upend systems they believed were depriving people of agency and purpose.” Such calls haven’t gone silent in 2020, just as The Plague — one of Camus’ writings in response to revolutionary existentialism — has only gained relevance in a time of global pandemic.
Last month the Boston Review‘s Carmen Lea Dege considered the recent comeback of the thought, exemplified in different ways by Camus, Sartre, and others, that “rejected religious and political dogma, expressed scorn for academic abstraction, and focused on the finitude and absurdity of human existence.” This resurgence of interest “is not entirely surprising. The body of work we now think of as existentialist emerged during the first half of the twentieth century in conflict-ridden Germany and France, where uncertainty permeated every dimension of society.” As much as our societies have changed since then, uncertainty has a way of returning.
Today “we define ourselves and others on the basis of class, religion, race, and nationality, or even childhood influences and subconscious drives, to gain control over the contingencies of the world and insert ourselves in the myriad ways people have failed and succeeded in human history.” But the existentialists argued that “this control is illusory and deceptive,” an “alluring distraction from our own fragility” that ultimately “corrodes our ability to live well.” For the existentialists, pursuit of good life first demands an acceptance of not just fragility but futility, meaninglessness, absurdity, and ambiguity, among other conditions that strike us as deeply unacceptable. As Camus put it, we must imagine Sisyphus happy. But can we?
Who among us hasn’t wished to be as efficient as a computer? While computers seem to do everything at once, we either flit or plod from task to task, often getting sidetracked or even lost. At this point most have relinquished the dream of true “multitasking,” which turns out to lie not only beyond the reach of humans but, technically speaking, beyond the reach of computers as well. “Done right, computers move so fluidly between their various responsibilities, they give the illusion of doing everything simultaneously,” says the narrator of the animated TED-Ed lesson above. But in reality, even they do one thing at a time; what, then, can we humans learn from how they’re programmed to prioritize and switch between their many tasks?
A computer operating system has an element called a “scheduler,” which “tells the CPU how long to work on each task before switching.” Schedulers work quite well these days, but “even computers get overwhelmed sometimes.” This used to happen to the open-source operating system Linux, which “would rank every single one of its tasks in order of importance, and sometimes spent more time ranking tasks than doing them. The programmers’ counterintuitive solution was to replace this full ranking with a limited number of priority ‘buckets,'” replacing a precise priority ordering with a broader low-medium-high kind of grouping. This turned out to be a great improvement: “The system was less precise about what to do next, but more than made up for it by spending more time making progress.”
The lesson for those of us who habitually list and prioritize our tasks is obvious: “All the time you spend prioritizing your work is time you aren’t spending doing it,” and “giving up on doing things in the perfect order may be the key to getting them done.” In the case of e-mail, bane of many a 21st-century existence, “Insisting on always doing the very most important thing first could lead to a meltdown. Waking up to an inbox three times fuller than normal could take nine times longer to clear.
You’d be better off replying in chronological order, or even at random.” Robert Pirsig memorably articulated this in Zen and the Art of Motorcycle Maintenance, whose main character offers advice to his son frustrated by the task of writing a letter home from their road trip:
I tell him getting stuck is the commonest trouble of all. Usually, I say, your mind gets stuck when you’re trying to do too many things at once. What you have to do is try not to force words to come. That just gets you more stuck. What you have to do now is separate out the things and do them one at a time. You’re trying to think of what to say and what to say first at the same time and that’s too hard. So separate them out. Just make a list of all the things you want to say in any old order. Then later we’ll figure out the right order.
We don’t write many letters home these days, of course, and even e-mail may no longer pose the direst threat to our time management. More of us blame our lack of productivity on the interruptions of instant messaging in all its forms, from texting to social media, another problem with an equivalent in computing. That a computer can be interrupted by any number of the processes it runs necessitated the development of a procedure called “interrupt coalescing,” according to which, “rather than dealing with things as they come up,” the system “groups these interruptions together based on how long they can afford to wait.” Even if we can’t eliminate interruptions in our lives, we can group them: “If no notification or e-mail requires a response more urgently than once an hour, say, then that’s exactly how often you should check them — no more.”
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