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Machines Are on the Verge of Tackling Fermat’s Last Theorem—a Proof That Once Defied Them
Some people count down to new video games or Beyonce albums. Mathematicians can now also count down to April, when mathematician and programmer Kevin Buzzard will release and begin updating his newly-announced plans for a computer coded proof of Fermat’s Last Theorem. He has received a grant for this research, which is expected to take years and will likely be one of the most complex proofs to be computerized in this way.
17th century French mathematician Pierre de Fermat came up with this theorem many years ago, but was unable to prove it in his own lifetime. The theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. (Thank you to a keen-eyed reader who noticed we initially used subscript by error.)
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Gut bacteria could play role in kidney autoimmune disease, study shows
Right now, inside your digestive tract, there are trillions of bacteria, fungi, and viruses that form a tiny universe known as the gut microbiome. New research shows that certain bacteria can alter antibodies so much that they’re unrecognizable to the body’s defenses — potentially leading to immune friendly fire.
The bacteria, called Akkermansia muciniphila, can strip the sugar coating from IgA antibodies, immune proteins abundant in the gut. This transformation may play a key role in the development of IgA nephropathy, an autoimmune disease of the kidneys, according to a study published Wednesday in Science Translational Medicine.
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Why Is My Apartment So Dusty All the Time?
Walking into my apartment, you might think no one had been there for months. There is a thick layer of dust on nearly every surface — the dresser, the bookshelves, the mirrors. It gathers in the corners of my room, in long strings and fat clumps. Dusting doesn’t seem to help much, either: A surface I wipe down in the morning will be at least a little dusty by afternoon. In comparison, my parents’ house upstate is almost never dusty. I stayed there after they were away for months on a recent trip and marveled at how pristine the piano and coffee table were. It seemed unfair somehow. Was it me? My apartment? Is New York City just dustier than other places?
But Bostick did have some theories about why I felt so plagued by the stuff. He guessed (correctly) that I lived on the first or second floor of my building, and pointed out that most of the fine particle dust in the city comes from pollutants like combustion from cars. While we may not have as many cars per capita as other cities that are more suburban and spread out, we do live closer to them. (In certain neighborhoods, like the South Bronx, proximity to truck pollution is especially bad, driving high rates of asthma.) “In New York, your house is right on the street and the windows are one sidewalk away from traffic,” Bostick said. All those particles just waft right in. There are other possible factors at play: The buildings in New York are relatively old — the median age of buildings is around 90 years — and many of them lack new air-filtration systems. A lot of indoor air pollution also comes from cooking, which, again, settles differently in a tiny apartment compared to a huge suburban kitchen. “Think of how many people essentially live in their kitchens in New York,” Bostick said.
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Two brains: One visualizes too much, the other not at all | CNN
Mary Wathen has never had that experience. When the 43-year-old solicitor from Newent, England, recalls baking with her mother, no images come to mind. She cannot visualize herself as a child opening presents, her husband's face when he proposed, or even the birth of her children.
A year ago Wathen discovered that she and her mother use a rare form of processing called aphantasia â their brains don't form mental images to remember or imagine. (Phantasia is the Greek word for imagination.) "Until recently, I had no idea that other people did see images. I just assumed that everyone was like me," she said.
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Who Expects to Get Richer in 2024, by Generation and Gender
A survey of 600 high net worth individuals revealed differing wealth increase expectations across gender and age.
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An Ecology of Intimacies
At its best, an intimate relationship is a symbiote of mutual nourishment — a portable ecosystem of interdependent growth, undergirded by a mycelial web of trust and tenderness. One is profoundly changed by it and yet becomes more purely oneself as projections give way to presence and complexes are composted into candid relation.
In his slender and splendid book Twice Alive (public library), poet, geologist, and translator Forrest Gander draws from the natural world a poetic “ecology of intimacies,” reverencing lichens’ “supreme parsimony in drought” and the “long soft sarongs of moss” as a way “to recover the play of life itself.”
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How mastering the art of being alone can boost your mental health - New Scientist (No paywall)
Solitude is inevitable. Adults in the UK and US spend around one-third of their waking lives alone and that increases as we get older. In many places, we live alone in greater proportions than ever before. A recent survey of 75 countries shows that 17 of them have more than 25 per cent solo households.
As social creatures, research has historically pointed us away from time alone. But recently, more people are spending time away from the crowd, and even seem to crave it. Now, we have evidence as to why alone time can feel so good and may in fact be vital to your health and well-being. Moreover, we have…
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How ground-based astronomers overcome Earth's atmosphere
One of the most profoundly remarkable properties about our atmosphere is that it’s transparent to not only sunlight, but to starlight as well. As we turn our eyes skyward after the Sun goes down, a glittering tapestry of planets, stars, galaxies, and nebulae illuminates the heavens. If we want to view it, all we have to do is look with the proper tools.
But our view of what’s out there, from here on Earth, is limited in ways we rarely think about. Even on a cloudless night, any light coming to us from space must pass through over 100 kilometers (more than 60 miles) of atmosphere, which itself has continuous variations in density, temperature, and molecular composition. Any light coming in has to contend with the atmosphere, and even though the atmosphere is transparent, that light inevitably gets distorted.
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4 essential tactics for honing your leadership language
Every leader wants to give that speech. With victory all but out of reach, they want their words to rouse the team’s emotions and inspire them to overcome the the odds. You can practically hear the music swelling just thinking about it.
Such speeches make for storybook moments, but how a leader uses language in everyday situations can be just as, if not more, powerful. As Wharton School marketing professor Jonah Berger tells Big Think, “The most fascinating thing I’ve found from the work that we and others have done is that subtle shifts can have such a big impact.”
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How Vladimir Putin and Xi Jinping define democracy
Shortly after Xi Jinping was reelected as China’s head of state in 2022 — by a vote of 2,950 to zero — the Chinese foreign minister Qin Gang criticized U.S. President Joe Biden for contextualizing the event as part of a battle between Western democracies and non-Western autocracies. Gang proclaimed that China, alongside Vladimir Putin’s Russia, was “committed to promoting a multipolar world and greater democracy in international relations.”
Neither politician can be taken at their word, though. Gang’s career is predicated on his loyalty to Xi, for which he was rewarded a promotion to state councilor. Meanwhile, Biden hopes to imbue his reelection campaign against Donald Trump with a sense of existential dread. Motivated by the politics of their respective countries, neither is telling the full story.
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Thursday 28th March 2024