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  • richardmitnick 3:04 pm on January 22, 2023 Permalink | Reply
    Tags: "Why This Universe? Maybe It’s Not Special—Just Probable", "Wick rotation", Boyle and Turok believe the equation conducts a census of all conceivable cosmic histories., coauthored a new calculation about the relative likelihoods of different universes., Cosmologists have spent decades striving to understand why our universe is so stunningly vanilla., , If the Wick rotation would work for more than just black holes it’s irresistible to do the same with the cosmological properties of the whole universe.”, Latham Boyle-a physicist and cosmologist at the Perimeter Institute for Theoretical Physics, Neil Turok of the University of Edinburgh and Latham Boyle of the Perimeter Institute, , , The properties of our universe — smooth and flat-just a pinch of dark energy-are what we should expect to see according to a new calculation., The provocative conclusion rests on a mathematical trick involving switching to a clock that ticks with "imaginary numbers"., , Two physicists find that our universe has a higher entropy—and is therefore more likely—than alternative possible universes., WIRED   

    From “Quanta Magazine” : “Why This Universe? Maybe It’s Not Special—Just Probable” 

    From “Quanta Magazine”

    1.22.23
    Charlie Wood

    Two physicists find that our universe has a higher entropy—and is therefore more likely—than alternative possible universes.

    1
    The properties of our universe — smooth and flat-just a pinch of dark energy-are what we should expect to see according to a new calculation. Illustration: Kouzou Sakai/Quanta Magazine.

    Cosmologists have spent decades striving to understand why our universe is so stunningly vanilla. Not only is it smooth and flat as far as we can see, but it’s also expanding at an ever-so-slowly increasing pace, when naive calculations suggest that—coming out of the Big Bang—space should have become crumpled up by gravity and blasted apart by repulsive dark energy.

    To explain the cosmos’s flatness, physicists have added a dramatic opening chapter to cosmic history: They propose that space rapidly inflated like a balloon at the start of the Big Bang, ironing out any curvature.

    ___________________________________________________________________
    Inflation

    In physical cosmology, cosmic inflation, cosmological inflation is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10^−36 seconds after the conjectured Big Bang singularity to some time between 10^−33 and 10^−32 seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).

    Inflation theory was developed in the late 1970s and early 80s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Alexei Starobinsky, Alan Guth, and Andrei Linde won the 2014 Kavli Prize “for pioneering the theory of cosmic inflation.” It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe. Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.

    The detailed particle physics mechanism responsible for inflation is unknown. The basic inflationary paradigm is accepted by most physicists, as a number of inflation model predictions have been confirmed by observation; however, a substantial minority of scientists dissent from this position. The hypothetical field thought to be responsible for inflation is called the inflaton.

    In 2002 three of the original architects of the theory were recognized for their major contributions; physicists Alan Guth of M.I.T., Andrei Linde of Stanford, and Paul Steinhardt of Princeton shared the prestigious Dirac Prize “for development of the concept of inflation in cosmology”. In 2012 Guth and Linde were awarded the Breakthrough Prize in Fundamental Physics for their invention and development of inflationary cosmology.

    4
    Alan Guth, from M.I.T., who first proposed Cosmic Inflation.

    Alan Guth’s notes:
    Alan Guth’s original notes on inflation.
    ___________________________________________________________________
    And to explain the gentle growth of space following that initial spell of inflation, some have argued that our universe is just one among many less hospitable universes in a giant multiverse.

    Multiverse. Image credit: public domain, retrieved from https://pixabay.com/

    But now two physicists have turned the conventional thinking about our vanilla universe on its head. Following a line of research started by Stephen Hawking and Gary Gibbons in 1977, the duo has published a new calculation suggesting that the plainness of the cosmos is expected, rather than rare. Our universe is the way it is, according to Neil Turok of the University of Edinburgh and Latham Boyle of the Perimeter Institute for Theoretical Physics in Waterloo, Canada, for the same reason that air spreads evenly throughout a room: Weirder options are conceivable but exceedingly improbable.

    The universe “may seem extremely fine-tuned, extremely unlikely, but [they’re] saying, ‘Wait a minute, it’s the favored one,’” said Thomas Hertog, a cosmologist at the Catholic University of Leuven in Belgium.

    “It’s a novel contribution that uses different methods compared to what most people have been doing,” said Steffen Gielen, a cosmologist at the University of Sheffield in the United Kingdom.

    The provocative conclusion rests on a mathematical trick involving switching to a clock that ticks with “imaginary numbers”. Using the imaginary clock, as Hawking did in the ’70s, Turok and Boyle could calculate a quantity, known as entropy, that appears to correspond to our universe. But the imaginary time trick is a roundabout way of calculating entropy, and without a more rigorous method, the meaning of the quantity remains hotly debated. While physicists puzzle over the correct interpretation of the entropy calculation, many view it as a new guidepost on the road to the fundamental, quantum nature of space and time.

    “Somehow,” Gielen said, “it’s giving us a window into perhaps seeing the microstructure of space-time.”

    Imaginary Paths

    Turok and Boyle, frequent collaborators, are renowned for devising creative and unorthodox ideas about cosmology. Last year, to study how likely our universe may be, they turned to a technique developed in the ’40s by the physicist Richard Feynman.

    Aiming to capture the probabilistic behavior of particles, Feynman imagined that a particle explores all possible routes linking start to finish: a straight line, a curve, a loop, ad infinitum. He devised a way to give each path a number related to its likelihood and add all the numbers up. This “path integral” technique became a powerful framework for predicting how any quantum system would most likely behave.

    As soon as Feynman started publicizing the path integral, physicists spotted a curious connection with thermodynamics, the venerable science of temperature and energy. It was this bridge between quantum theory and thermodynamics that enabled Turok and Boyle’s calculation.

    3
    The South African physicist and cosmologist Neil Turok is a professor at the University of Edinburgh.Photograph: Gabriela Secara/Perimeter Institute.

    Thermodynamics leverages the power of statistics so that you can use just a few numbers to describe a system of many parts, such as the gajillion air molecules rattling around in a room. Temperature, for instance—essentially the average speed of air molecules—gives a rough sense of the room’s energy. Overall properties like temperature and pressure describe a “macrostate” of the room.

    But a macrostate is a crude account; air molecules can be arranged in a tremendous number of ways that all correspond to the same macrostate. Nudge one oxygen atom a bit to the left, and the temperature won’t budge. Each unique microscopic configuration is known as a microstate, and the number of microstates corresponding to a given macrostate determines its entropy.

    Entropy gives physicists a sharp way of comparing the odds of different outcomes: The higher the entropy of a macrostate, the more likely it is. There are vastly more ways for air molecules to arrange themselves throughout the whole room than if they’re bunched up in a corner, for instance. As a result, one expects air molecules to spread out (and stay spread out). The self-evident truth that probable outcomes are probable, couched in the language of physics, becomes the famous second law of thermodynamics: that the total entropy of a system tends to grow.

    The resemblance to the path integral was unmistakable: In thermodynamics, you add up all possible configurations of a system. And with the path integral, you add up all possible paths a system can take. There’s just one rather glaring distinction: Thermodynamics deals in probabilities, which are positive numbers that straightforwardly add together. But in the path integral, the number assigned to each path is complex, meaning that it involves the imaginary number i, the square root of −1. Complex numbers can grow or shrink when added together—allowing them to capture the wavelike nature of quantum particles, which can combine or cancel out.

    Yet physicists found that a simple transformation can take you from one realm to the other. Make time imaginary (a move known as a “Wick rotation” after the Italian physicist Gian Carlo Wick), and a second i enters the path integral that snuffs out the first one, turning imaginary numbers into real probabilities. Replace the time variable with the inverse of temperature, and you get a well-known thermodynamic equation.

    This Wick trick led to a blockbuster finding by Hawking and Gibbons in 1977, at the end of a whirlwind series of theoretical discoveries about space and time.

    The Entropy of Space-Time

    Decades earlier, Albert Einstein’s General Theory of Relativity had revealed that space and time together form a unified fabric of reality—space-time—and that the force of gravity is really the tendency for objects to follow the folds in space-time. In extreme circumstances, space-time can curve steeply enough to create an inescapable Alcatraz known as a black hole.

    In 1973, Jacob Bekenstein advanced the heresy [Physical Review D (below)] that black holes are imperfect cosmic prisons. He reasoned that the abysses should absorb the entropy of their meals, rather than deleting that entropy from the universe and violating the second law of thermodynamics. But if black holes have entropy, they must also have temperatures and must radiate heat.

    A skeptical Stephen Hawking tried to prove Bekenstein wrong, embarking on an intricate calculation of how quantum particles behave in the curved space-time of a black hole. To his surprise, in 1974 he found that black holes do indeed radiate. Another calculation confirmed Bekenstein’s guess: A black hole has entropy equal to one-quarter the area of its event horizon—the point of no return for an infalling object.

    In the years that followed, the British physicists Malcolm Perry and Gibbons, and later Gibbons and Hawking, arrived at the same result from another direction. They set up a path integral, in principle adding up all the different ways space-time might bend to make a black hole. Next, they Wick-rotated the black hole, marking the flow of time with imaginary numbers, and scrutinized its shape. They discovered that in the imaginary time direction the black hole periodically returned to its initial state. This Groundhog Day-like repetition in imaginary time gave the black hole a sort of stasis that allowed them to calculate its temperature and entropy.

    They might not have trusted the results if the answers had not precisely matched those calculated earlier by Bekenstein and Hawking. By the end of the decade, their collective work had yielded a startling notion: The entropy of black holes implied that space-time itself is made of tiny, rearrangeable pieces, much as air is made of molecules. And miraculously, even without knowing what these “gravitational atoms” were, physicists could count their arrangements by looking at a black hole in imaginary time.

    “It’s that result which left a deep, deep impression on Hawking,” said Hertog, Hawking’s former graduate student and longtime collaborator. Hawking immediately wondered if the Wick rotation would work for more than just black holes. “If that geometry captures a quantum property of a black hole,” Hertog said, “then it’s irresistible to do the same with the cosmological properties of the whole universe.”

    Counting All Possible Universes

    Right away, Hawking and Gibbons Wick-rotated one of the simplest imaginable universes—one containing nothing but the dark energy built into space itself. This empty, expanding universe, called a “de Sitter” space-time, has a horizon, beyond which space expands so quickly that no signal from there will ever reach an observer in the center of the space. In 1977, Gibbons and Hawking calculated that, like a black hole, a de Sitter universe also has an entropy equal to one-fourth its horizon’s area. Again, space-time seemed to have a countable number of microstates.

    But the entropy of the actual universe remained an open question. Our universe is not empty; it brims with radiating light and streams of galaxies and dark matter. Light drove a brisk expansion of space during the universe’s youth, then the gravitational attraction of matter slowed things to a crawl during cosmic adolescence. Now dark energy appears have taken over, driving a runaway expansion. “That expansion history is a bumpy ride,” Hertog said. “To get an explicit solution is not so easy.”

    Over the past year or so, Boyle and Turok have built just such an explicit solution. First, in January, while playing with toy cosmologies, they noticed that adding radiation to de Sitter space-time didn’t spoil the simplicity required to Wick-rotate the universe.

    Then over the summer they discovered that the technique would withstand even the messy inclusion of matter. The mathematical curve describing the more complicated expansion history still fell into a particular group of easy-to-handle functions, and the world of thermodynamics remained accessible. “This Wick rotation is murky business when you move away from very symmetric space-time,” said Guilherme Leite Pimentel, a cosmologist at the Scuola Normale Superiore in Pisa, Italy. “But they managed to find it.”

    By Wick-rotating the roller-coaster expansion history of a more realistic class of universes, they got a more versatile equation for cosmic entropy. For a wide range of cosmic macrostates defined by radiation, matter, curvature, and a dark energy density (much as a range of temperatures and pressures define different possible environments of a room), the formula spits out the number of corresponding microstates. Turok and Boyle posted their results online in early October.

    3
    Latham Boyle, a physicist and cosmologist at the Perimeter Institute for Theoretical Physics, coauthored a new calculation about the relative likelihoods of different universes. Photograph: Gabriela Secara/Perimeter Institute.

    Experts have praised the explicit, quantitative result. But from their entropy equation, Boyle and Turok have drawn an unconventional conclusion about the nature of our universe. “That’s where it becomes a little more interesting, and a little more controversial,” Hertog said.

    Boyle and Turok believe the equation conducts a census of all conceivable cosmic histories. Just as a room’s entropy counts all the ways of arranging the air molecules for a given temperature, they suspect their entropy counts all the ways one might jumble up the atoms of space-time and still end up with a universe with a given overall history, curvature, and dark energy density.

    Boyle likens the process to surveying a gigantic sack of marbles, each a different universe. Those with negative curvature might be green. Those with tons of dark energy might be cat’s-eyes, and so on. Their census reveals that the overwhelming majority of the marbles have just one color—blue, say—corresponding to one type of universe: one broadly like our own, with no appreciable curvature and just a touch of dark energy. Weirder types of cosmos are vanishingly rare. In other words, the strangely vanilla features of our universe that have motivated decades of theorizing about cosmic inflation and the multiverse may not be strange at all.

    Counting Confusion

    Boyle and Turok have calculated an equation that counts universes. And they’ve made the striking observation that universes like ours seem to account for the lion’s share of the conceivable cosmic options. But that’s where the certainty ends.

    The duo make no attempt to explain what quantum theory of gravity and cosmology might make certain universes common or rare. Nor do they explain how our universe, with its particular configuration of microscopic parts, came into being. Ultimately, they view their calculation as more of a clue to which sorts of universes are preferred than anything close to a full theory of cosmology. “What we’ve used is a cheap trick to get the answer without knowing what the theory is,” Turok said.

    Their work also revitalizes a question that has gone unanswered since Gibbons and Hawking first kicked off the whole business of space-time entropy: What exactly are the microstates that the cheap trick is counting?

    “The key thing here is to say that we don’t know what that entropy means,” said Henry Maxfield, a physicist at Stanford University who studies quantum theories of gravity.

    At its heart, entropy encapsulates ignorance. For a gas made of molecules, for instance, physicists know the temperature—the average speed of particles—but not what every particle is doing; the gas’s entropy reflects the number of options.

    After decades of theoretical work, physicists are converging on a similar picture for black holes. Many theorists now believe that the area of the horizon describes their ignorance of the stuff that’s fallen in—all the ways of internally arranging the building blocks of the black hole to match its outward appearance. (Researchers still don’t know what the microstates actually are; ideas include configurations of the particles called gravitons or the strings of string theory.)

    4
    A recent calculation by Ted Jacobson, top, and Batoul Banihashemi of the University of Maryland offers a possible interpretation of the entropy of de Sitter space. Courtesy of Ted Jacobson; Courtesy of Batoul Banihashemi.

    But when it comes to the entropy of the universe, physicists feel less certain about where their ignorance even lies.

    In April, two theorists attempted to put cosmological entropy on a firmer mathematical footing. Ted Jacobson, a physicist at the University of Maryland renowned for deriving Einstein’s theory of gravity from black hole thermodynamics, and his graduate student Batoul Banihashemi explicitly defined the entropy of a (vacant, expanding) de Sitter universe. They adopted the perspective of an observer at the center. Their technique, which involved adding a fictitious surface between the central observer and the horizon, then shrinking the surface until it reached the central observer and disappeared, recovered the Gibbons and Hawking answer that entropy equals one-quarter of the horizon area. They concluded that the de Sitter entropy counts all possible microstates inside the horizon.

    Turok and Boyle calculate the same entropy as Jacobson and Banihashemi for an empty universe. But in their new calculation pertaining to a realistic universe filled with matter and radiation, they get a much larger number of microstates—proportional to volume and not area. Faced with this apparent clash, they speculate that the different entropies answer different questions: The smaller de Sitter entropy counts microstates of pure space-time bounded by a horizon, while they suspect their larger entropy counts all the microstates of a space-time filled with matter and energy, both inside and outside the horizon. “It’s the whole shebang,” Turok said.

    Ultimately, settling the question of what Boyle and Turok are counting will require a more explicit mathematical definition of the ensemble of microstates, analogous to what Jacobson and Banihashemi have done for de Sitter space. Banihashemi said she views Boyle and Turok’s entropy calculation “as an answer to a question that is yet to be fully understood.”

    As for more established answers to the question “Why this universe?” cosmologists say inflation and the multiverse are far from dead. Modern inflation theory, in particular, has come to solve more than just the universe’s smoothness and flatness. Observations of the sky match many of its other predictions. Turok and Boyle’s entropic argument has passed a notable first test, Pimentel said, but it will have to nail other, more detailed data to more seriously rival inflation.

    As befits a quantity that measures ignorance, mysteries rooted in entropy have served as harbingers of unknown physics before. In the late 1800s, a precise understanding of entropy in terms of microscopic arrangements helped confirm the existence of atoms. Today, the hope is that if the researchers calculating cosmological entropy in different ways can work out exactly what questions they’re answering, those numbers will guide them toward a similar understanding of how Lego bricks of time and space pile up to create the universe that surrounds us.

    “What our calculation does is provide huge extra motivation for people who are trying to build microscopic theories of quantum gravity,” Turok said. “Because the prospect is that that theory will ultimately explain the large-scale geometry of the universe.”

    “It’s a very intriguing result,” Hertog said. But “it raises more questions than it answers.”

    Physical Review D 1973
    posted their results online 2022

    See the full article here .

    Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct. Use “Reply”.

    five-ways-keep-your-child-safe-school-shootings

    Please help promote STEM in your local schools.

    Stem Education Coalition

    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 1:51 pm on January 22, 2023 Permalink | Reply
    Tags: "The Hunt for the Dark Web’s Biggest Kingpin Part 1 - The Shadow", Crime, The largest digital drug and crime bazaar in history known as "AlphaBay", The notorious "Alpha02" oversaw millions of dollars a day in online narcotic sales. For cybercrime detectives he was public enemy number one—and a total mystery., WIRED   

    From “WIRED” : “The Hunt for the Dark Web’s Biggest Kingpin Part 1 – The Shadow” 

    From “WIRED”

    10.25.22 [Just found this.]
    Andy Greenberg

    Adapted from Andy’s new book Tracers in the Dark: The Global Hunt for the Crime Lords of Cryptocurrency

    The notorious “Alpha02” oversaw millions of dollars a day in online narcotic sales. For cybercrime detectives he was public enemy number one—and a total mystery.

    1
    Illustration: Hokyoung Kim.

    On the morning of July 5, 2017, a gray Toyota Camry slowly turned into the cul-de-sac of a quiet neighborhood in Bangkok—a moderately upscale subdivision on the western edge of the city, where the pulsating capital’s downtown high-rises began to flatten out into highways and canals snaking through tropical forest and farmlands.

    Behind the wheel sat a woman who went by the nickname Nueng. A slight, 46-year-old agent of the Royal Thai Police with a short, boyish haircut, she wore a white polo shirt and black pants rather than her usual military-style uniform. Both she and the female officer beside her in the passenger seat were working undercover.

    2
    This story is excerpted from the forthcoming book Tracers in the Dark: The Global Hunt for the Crime Lords of Cryptocurrency, available November 15, 2022, from Doubleday. Courtesy of Penguin Random House.

    Nueng’s heart pounded. For more than two years, law enforcement agents from around the world had been hunting the dark-web mastermind known as “Alpha02”, a shadowy figure who oversaw millions of dollars a day in narcotics sales and had built the largest digital drug and crime bazaar in history, known as “AlphaBay”. Now, a coordinated take-down and sting involving no fewer than six countries’ agencies had tracked Alpha02 to Thailand. The operation had finally led to this quiet block in Bangkok, to the home of a 26-year-old Canadian named Alexandre Cazes. Nueng knew that the success of the plot to arrest Cazes and knock out this linchpin of the global underworld economy hinged on what she did in the next few moments.

    Trying to give the impression of an inexperienced driver, Nueng slowly rolled the car toward a model home and real estate office at the end of the cul-de-sac. She signaled to a security guard outside the house that she had taken a wrong turn and needed to pull a 180. She heard him shout at her to back directly out instead, that the street was too narrow for a three-point turn.

    Nueng quickly muttered a nearly silent prayer—an adapted, high-speed plea to the holy trinity of the Buddha, his teachings, and all the monks and nuns in his service. “Dear Buddha, please bless me with success,” she whispered in Thai. “Dear Dhamma, please bless me with success. Dear Sangha, please bless me with success.”

    Then she put the car in reverse, turned the wheel to the left, and ever so gently—almost in slow motion—slammed the Toyota’s fender into Alexandre Cazes’ front gate.

    CHAPTER 1
    ALPHA02

    Around 18 months earlier, Robert Miller sat in the US Drug Enforcement Administration’s wiretap room in Fresno, California, spending another painfully boring day listening in on the life of one of the DEA’s endless supply of narcotics targets in California’s Central Valley.

    All Miller ever wanted was to be on a SWAT team. At the academy, instructors had praised him for his instinctive judgment and thoroughness—how, in training raids on the academy’s mock-ups of drug dens, he always meticulously cleared his corners and covered his blind spots. And when the young DEA agent was assigned to the agency’s field office in Fresno right after graduation, he had high hopes it would put him where he wanted to be: making arrests, carrying out search warrants, “hitting doors,” as he put it. (Miller’s name and some personal details have been changed, per his request.)

    The sunbaked agricultural city in the middle of California had long served as a corridor for cocaine, heroin, weed, and methamphetamine smugglers, as traffickers from the southern border made their way to buyers in the Northwest and on the East Coast. Agents spent their days carrying out undercover buy-and-busts, following trucks packed with dope along Highway 99 and tracking, raiding, and arresting cartel operators.

    But not long after he moved to Fresno, Miller injured his foot and his shoulder while rock climbing. Both injuries required surgery. There would be no SWAT team, no “hitting doors”—not, at least, for the two years it would take to recover.

    So Miller was assigned to surveillance. He’d stake out targets from his car or sit in the office’s wiretap room, listening to suspects’ phone calls and reading their texts for weeks or sometimes months on end. The work was often mind-numbingly mundane. “Ninety-nine percent boredom and 1 percent excitement,” as he remembers it.

    At one point in 2013, Miller’s partner on a surveillance assignment suggested they try to work on a new sort of case. She had heard about a booming drug market on the dark web called Silk Road—a site where anyone could connect through the anonymity software Tor and spend bitcoins to buy any drug imaginable—and its pseudonymous creator, the Dread Pirate Roberts. But when Miller asked his superiors about the site, he was told that teams in New York and Baltimore were already on it. Not long after, while Miller was on a surveillance stakeout in his car in a mall parking lot, his phone buzzed with an alert that the notorious market had been busted. The Dread Pirate Roberts turned out to be a 29-year-old Texan with no criminal record named Ross Ulbricht. He had been arrested in the science fiction section of San Francisco’s Glen Park Public Library with his laptop open and logged in to Silk Road.

    Two long years later, in early 2016, Miller’s boss came into the wiretap room and asked whether Miller wanted to join a different team. Someone in the office had remembered Miller’s inquiry into Silk Road. A local assistant US attorney had assembled a group to focus on dark-web crime, and he was looking for volunteers from all the federal agencies clustered around Courthouse Park in Fresno’s downtown square: the Internal Revenue Service, Homeland Security Investigations, and the Drug Enforcement Administration. The assignment, Miller knew, was pretty much the opposite of the SWAT team. But at least it would be something new. “OK,” he said. “I’ll do it.”

    Grant Rabenn, the young prosecutor at the helm of Fresno’s dark-web strike force, laid out a set of modest initial goals for the group: They would be going after individual money launderers and drug dealers, not kingpins and masterminds. “We are not the Southern District of New York. We are in a dusty town in the Central Valley of California,” as Rabenn put it. “Let’s hit singles before we try to go for a home run.”

    That humble starting point was fine with Miller, who had little idea of how the dark-web drug trade even worked. When Rabenn asked Miller to start making undercover heroin buys, he couldn’t figure out how to buy bitcoins, let alone the drugs themselves. He drove two and a half hours to San Jose to find a physical bitcoin ATM rather than simply use an online exchange. Even then, he discovered that after transaction fees he could purchase only half a gram of heroin instead of the 2 grams he’d planned on.

    But slowly, as Miller poked around the dark web and perused the various markets, he got a feel for the post-Silk Road online drug economy. He soon came to see that it was dominated by a single entity: “AlphaBay”.

    AlphaBay had first appeared in late 2014, just one in the broad scrum of markets vying for a share of the growing dark-web criminal trade. But the site’s pseudonymous administrator, Alpha02, seemed cannier than those behind many of the competing markets. Alpha02 was a well known if not exceptionally talented “carder,” a cyber criminal hacker focused on credit card theft and fraud. He’d become a significant player on Tor Carding Forum, a dark-web site where hackers traded in stolen data. He’d even sold his own 16-page “University of Carding Guide,” designed to teach beginners the tricks of the trade, like how to “social-engineer” customer service representatives at banks, calling from spoofed telephone numbers to deceive them into approving fraudulent transactions.

    In its first months online, AlphaBay seemed destined to serve much the same hacker clientele. It was devoted almost exclusively to cybercriminal wares, such as stolen account logins and credit card data. But as Alpha02 bootstrapped the site from its carder origins, its portfolio of vendors quickly expanded to offer the dark web’s more lucrative contraband: ecstasy, marijuana, meth, cocaine, and heroin, all shipped through the mail. Soon it became clear that Alpha02’s grand vision was to unite two spheres of the dark web that had, until then, been somewhat distinct—one devoted to cybercrime and the other to drugs—to create a single mega-market. AlphaBay’s goal, he declared, was “to become the largest eBay-style underworld marketplace.”

    Silk Road’s Dread Pirate Roberts had espoused a kind of anarcho-capitalist ideal, describing his site as a “movement” or a “revolution” bent on liberating mankind from oppressive government control of commerce and limiting sellers, at least in theory, to offering only “victimless” products. Alpha02, by contrast, seemed to adopt a much less high-minded focus on the bottom line. Aside from a ban on child abuse materials and murder for hire, the only rule Alpha02 imposed on AlphaBay’s vendors was that they not sell data or accounts stolen from Russia or other former Soviet states, or infect those countries’ computers with malware. This prohibition, common among cybercriminals from that part of the world, was typically designed to avoid trouble from Russian law enforcement—a kind of “don’t shit where you sleep” principle. For Miller and other federal agents and prosecutors sniffing around the site, it also suggested that AlphaBay and its mysterious founder were likely based in Russia—an impression cemented by Alpha02’s signature in messages on the site’s forums: “Будьте в безопасности, братья,” Russian for “Be safe, brothers.”

    In an interview in April 2015 with the news site and dark-web directory DeepDotWeb, Alpha02 reassured his users that he and his site were beyond the reach of any Silk Road-style seizure. “I am absolutely certain my opsec is secure,” he wrote, using the shorthand for “operational security,” and added, “I live in an offshore country where I am safe.”

    Throughout that interview, Alpha02 wrote in the style of a corporate press release: “We have made sure to have created a stable & fast marketplace web application which has been built with security in mind right from the start,” he wrote, adding, “We would like to assure all of our users (both vendors & buyers) that their security, privacy and anonymity rank first place in our priorities list.”

    What Alpha02 lacked in political inspiration he seemed to make up for in technological aspiration and coding competency. He boasted about features that included auction-style bidding, search tools that helped fraudsters comb through stolen data to carefully choose their victims, and a multi-signature transaction scheme designed to reassure users that it would be far harder for law enforcement or rogue staff to steal funds held in escrow.

    “We want to have every imaginable possible feature to be the #1 market,” he wrote to DeepDotWeb. On each page of AlphaBay, he’d signed his work: “proudly designed by Alpha02.”

    When a judge imposed a double life sentence on the Silk Road’s Ross Ulbricht in May 2015, she told the court that the draconian sentence was partly meant to scare off future dark-web drug buyers, dealers, and administrators. By the time of AlphaBay’s rise, that unprecedented punishment seemed to have had the opposite effect. A study in The British Journal of Criminology found that sales on what was then the top dark-web site, Agora, more than doubled in the days following the news of Ulbricht’s sentencing, to more than $350,000 a day. The study’s author, trying to interpret that unexpected increase, reasoned that by imposing such a shocking prison term, the judge had only generated new awareness of the dark-web drug trade. Rather than deterring users, the judge seemed to have created a massive advertisement for the world’s burgeoning cryptocurrency black markets.

    Alpha02 was hardly fazed by the news. Following Ulbricht’s sentencing, in an interview with Vice’s tech news site, Motherboard, he momentarily affected a revolutionary posture, picking up the Dread Pirate Roberts’ torch. “Courts can stop a man, but they can’t stop an ideology,” he wrote. “Darknet markets will always be around, until the war on drugs stops.”

    But in response to other questions, AlphaBay’s boss seemed to ditch the torch and speak more plainly. “We have to carry on with business,” he wrote. “We all need money to eat.”

    By the fall of 2015, AlphaBay was the biggest market on the dark web. Agora’s administrators had taken their site offline that August, citing concerns that a vulnerability in Tor, the online anonymity system that powered the dark web, might be used to locate Agora’s servers. AlphaBay appeared to have no such security flaw. As it absorbed Agora’s tens of thousands of buyers and vendors, the growing crowd of law enforcement agents around the world surveilling the site could find no coding or opsec slipups to give them the slightest clue as to where they might find its servers, not to mention its founder.

    Shortly before AlphaBay took over the dark web’s top spot, Alpha02 had changed his username on the site to merely “admin” and announced that he would no longer accept any private messages sent to him by anyone other than AlphaBay’s staff. Instead, he left much of the site’s communications work to his second-in-command and head of security, a figure who went by the pseudonym “DeSnake”.

    The Alpha02 moniker had served its purpose, lending the site its initial credibility. Now the person behind it intended, like discreet criminal bosses the world over, to slip into the shadows, raking in his fortune as quietly and anonymously as possible.

    That fortune was, by the time of Alpha02’s name change, growing at an unprecedented rate: By October 2015, AlphaBay had more than 200,000 users and more than 21,000 product listings for drugs, compared to just 12,000 listings on Silk Road at its peak. Sometime around the middle of 2016, AlphaBay surpassed Agora’s peak sales rate of $350,000 a day, according to researchers at Carnegie Mellon. It had become not only the biggest black market on the dark web, but the biggest cryptocurrency black market of all time. And it was still growing wildly.

    For Grant Rabenn, the Fresno-based prosecutor, it was clear that Alpha02 was now the most wanted man on the dark web; Rabenn compared his notoriety among digital crime investigators to that of Osama bin Laden. AlphaBay and Alpha02 were invoked at every law enforcement conference on cybercrime, every interagency meeting, every training event, Rabenn says. And as the target on Alpha02’s back loomed larger, so too did the unspoken fear that this mastermind might stay a step ahead of them indefinitely.

    “Is this person just a pure genius who’s figured out all of the possible mistakes?” Rabenn remembers asking himself. “Has this individual found the perfect country with the right IT infrastructure to run a marketplace, and he’s able to bribe the officials there so we’ll never touch him?

    “As every day passed there was, more and more, a sense that this might be the special one,” Rabenn says. “You begin to wonder: Is this the Michael Jordan of the dark web?”

    But Rabenn followed these discussions of Alpha02 from a distance. The idea that his Fresno team might actually take on the Michael Jordan of the dark web had never occurred to him. “It’s not expected for people like us,” he says simply, “to go after a site like that.”

    CHAPTER 2
    THE TIP

    Before Grant Rabenn became a federal prosecutor, his second job out of law school was at a boutique firm in Washington, DC, devoted to defending white-collar criminals. The young, olive-skinned lawyer with dark hair and a Hollywood smile ended up representing Russian oligarchs and corporate executives accused of bribing foreign governments. “Very interesting, wealthy people trying to hide their assets and avoid scrutiny,” as he described them, or alternatively, “James Bond characters who are jet-setting around the world with suitcases full of cash.”

    Rabenn was captivated by these glimpses into a world of billions of dollars moving in invisible transactions. But he also found that he admired and envied the prosecutors on the other side of the table—the way they worked in the public interest and possessed a certain autonomy, choosing which cases they would pursue. So he began applying for Justice Department jobs, finally finding one in Fresno.

    Despite having grown up in Southern California, Rabenn couldn’t place Fresno on a map. But when he arrived at its DOJ office in 2011, he found what he’d always wanted: a place with almost no hierarchy or bureaucracy, where he was simply told to focus on money laundering and was otherwise given free rein. For the next few years, he and the local agents tackled fraud and extortion, child exploitation, corrupt cops, and, of course, drug trafficking—following illicit trails of money wherever they led. “We were just running and gunning,” Rabenn says of those prolific years with a boyish enthusiasm.

    Rabenn’s money-laundering cases often began with the stream of suspicious activity reports that banks were required to file under the Bank Secrecy Act. By mid-2013, Rabenn found that more and more of those reports were being triggered by financial transfers out of crypto exchanges, platforms where users could trade digital currency for traditional money like dollars, euros, or yen. The banks often suspected that these currency swaps were cash-outs of dirty digital profits. So Rabenn immersed himself in dozens of hours of YouTube videos to understand this still new currency called Bitcoin, its mechanics, and how it seemed to be powering an anonymous underworld of online commerce.

    Criminals flocked to these dark markets because the cryptocurrency was widely believed to be anonymous and untraceable. Sure, every transaction was immortalized on Bitcoin’s blockchain, an unforgeable, unchangeable, and altogether public ledger. But that ledger recorded only which bitcoins resided at which Bitcoin addresses—long, unique strings of letters and numbers—at any given moment. In theory, at least, that meant buyers and sellers of illicit goods on opposite sides of the globe could send one another cash payments from behind the mask of those cryptic addresses without revealing any hint of their real-world identities.

    But just as cryptocurrency-based platforms like AlphaBay opened up vast new global markets to criminals, they also opened up huge new opportunities for law enforcement, as Rabenn quickly realized. The dark web presented him with the chance to work cases on a scale that would otherwise be impossible in Fresno: As long as a dark-web drug dealer could be coaxed into sending a package to the Eastern District of California, the crime officially occurred in his jurisdiction.

    Rabenn had no real idea how to pierce the veil of the blockchain’s anonymity. But he figured that even dark-web dealers must sometimes make mistakes that could be caught through traditional buy-and-bust police work. For an ambitious young prosecutor, the possibility was thrilling. “I wasn’t necessarily happy with just prosecuting drug mules driving meth up the 99 freeway,” he says. If he could arrange an undercover buy online and somehow identify the seller, he could arrest dealers all over the country. “All I have to do is order dope from them, and then we can go get them. And that’s what we did.”

    In 2014, Rabenn began forming his dark-web strike force, inviting local investigators from Fresno’s Homeland Security Investigations and IRS Criminal Investigations offices to join. It was a small team of “odd ducks,” as he describes them—agents on the more cerebral side, content to work cases largely on a computer screen instead of kicking down doors like their Central Valley colleagues.

    By the time he recruited Robert Miller out of the DEA’s wiretap room, Rabenn’s team had already achieved some success with their undercover approach. They’d started by cracking down on a few so-called peer-to-peer exchangers—individuals who bought and sold bitcoins in the real world and were often used by dark-web dealers to cash out their dirty cryptocurrency. In several cases, they’d mined those exchangers’ Rolodexes for leads on the legal names of dealers who’d done business with them, tracked them down, and arrested them.

    But Rabenn had also begun to suspect that his original hunch was correct: Many of the dealers they targeted were indeed sloppy enough that agents could simply purchase drugs and look for clues either in their packaging or the vendors’ online profiles.

    Miller, starting his new assignment, assembled the usernames of AlphaBay’s top dealers of heroin and the powerful synthetic opioid fentanyl, and he began to buy from them one by one. As the packages arrived, triple-sealed in silver Mylar and plastic, Miller and the team scrutinized both the shipments and their sellers’ online presence. They found that one vendor had made an elementary mistake: He’d linked his PGP key—the unique file that allowed him to exchange encrypted messages with customers—with his email address on the PGP key server that stores a catalog of users’ identities.

    Miller and Rabenn quickly tied that email to the dealer’s social media accounts and real name. They learned that he was based in New York. Miller then found fingerprints on a package of heroin sent from one of his accounts, which matched those of another New York man. Finally, Miller worked with postal inspectors to get photos taken by a post office self-service kiosk. The photos showed the second New Yorker putting a dope shipment in the mail. Miller and a team of agents flew across the country, searched the two men’s homes, and arrested them both.

    The same simple PGP trick allowed Miller to find the real name of another dark-web opiates dealer—which turned out to be part of his dark-web handle, written backward—and caught him shipping dope, again using evidence from a post office kiosk camera. When agents raided the man’s home in San Francisco, Miller says, they found piles of fentanyl and heroin powder sitting on tables and in open plastic containers.

    Rabenn’s team was now on a roll, building significant cases—and even a reputation. When Miller ordered a package of opiates addressed to Fresno, he was amused when his San Francisco suspect warned him that a particularly aggressive group of feds operating out of the Central Valley seemed to be targeting players on the dark web and that he’d better watch his back.

    But Miller and Rabenn didn’t kid themselves: Busting a few of AlphaBay’s sloppier dealers wasn’t any more likely to topple that black market than the DEA was to defeat Mexican cartels by chasing yet another meth mule up Highway 99.

    By November 2016, Miller was ready to try something new again. He’d achieved a couple of decent dark-web busts, but he didn’t love the paperwork or the weeks spent in front of a screen. His shoulder and foot had finally recovered. Perhaps it wasn’t too late to get onto the SWAT team after all.
    Most Popular

    Then, one afternoon, Miller returned to the office after picking up lunch, his In-N-Out Burger bag still in hand, to find an email from an intriguing stranger.

    The email explained that the sender had been googling dark-web arrests, looking for a law enforcement contact. They’d tried the FBI tip line, but no one had responded. They’d tried Homeland Security—no luck there either. Finally, they’d found Miller’s contact information in one of the Fresno team’s criminal indictments of an AlphaBay drug dealer.

    So the stranger had decided to try getting in touch with Miller. And now they were ready to share a tip about who Alpha02 might really be.

    Continued in part 2: On the trail of a mastermind, a tip leads detectives to a suspect in Bangkok—and to the daunting task of tracing his millions in cryptocurrency.

    See the full article here .

    Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct. Use “Reply”.

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  • richardmitnick 1:40 pm on January 16, 2023 Permalink | Reply
    Tags: "A Teenager Solved a Stubborn Prime Number ‘Look-Alike’ Riddle", "Carmichael numbers"—strange entities that mimic the primes., , Daniel Larsen, For more than a year and a half Larsen couldn’t stop thinking about a certain math problem: "Carmichael numbers"., He gets focused on something and it’s just bang bang bang until he succeeds., It was only in the mid-1990s that mathematicians proved there are infinitely many of them., Larsen holds the record for youngest person to publish a crossword in "The New York Times"., , Over a century ago in that quest for a fast powerful primality test mathematicians stumbled on a group of troublemakers—numbers that fool tests into thinking they’re prime even though they’re no, These pseudoprimes known as "Carmichael numbers" have been particularly difficult to grasp., WIRED   

    From “WIRED”: “A Teenager Solved a Stubborn Prime Number ‘Look-Alike’ Riddle” Daniel Larsen 

    From “WIRED”

    1.15.23
    Jordana Cepelewicz

    In his senior year of high school, Daniel Larsen proved a key theorem about “Carmichael numbers”—strange entities that mimic the primes.

    1
    After he posted his proof, Daniel Larsen enrolled at the Massachusetts Institute of Technology as a math major. Photograph: Katherine Taylor/Quanta Magazine.

    When Daniel Larsen was in middle school, he started designing crossword puzzles. He had to layer the hobby on top of his other interests: chess, programming, piano, violin. He twice qualified for the Scripps National Spelling Bee near Washington, DC, after winning his regional competition. “He gets focused on something, and it’s just bang, bang, bang, until he succeeds,” said Larsen’s mother, Ayelet Lindenstrauss. His first crossword puzzles were rejected by major newspapers, but he kept at it and ultimately broke in. To date, he holds the record for youngest person to publish a crossword in The New York Times, at age 13. “He’s very persistent,” Lindenstrauss said.

    Still, Larsen’s most recent obsession felt different, “longer and more intense than most of his other projects,” she said. For more than a year and a half Larsen couldn’t stop thinking about a certain math problem.

    It had roots in a broader question, one that the mathematician Carl Friedrich Gauss considered to be among the most important in mathematics: how to distinguish a prime number (a number that is divisible only by 1 and itself) from a composite number. For hundreds of years, mathematicians have sought an efficient way to do so. The problem has also become relevant in the context of modern cryptography, as some of today’s most widely used cryptosystems involve doing arithmetic with enormous primes.

    Over a century ago, in that quest for a fast, powerful primality test, mathematicians stumbled on a group of troublemakers—numbers that fool tests into thinking they’re prime, even though they’re not. These pseudoprimes known as “Carmichael numbers” have been particularly difficult to grasp. It was only in the mid-1990s, for instance, that mathematicians proved there are infinitely many of them. Being able to say something more about how they’re distributed along the number line has posed an even greater challenge.

    Then along came Larsen with a new proof about just that, one inspired by recent epochal work in a different area of number theory. At the time, he was just 17.

    The Spark

    Growing up in Bloomington, Indiana, Larsen was always drawn to mathematics. His parents, both mathematicians, introduced him and his older sister to the subject when they were young. (His sister is now pursuing a doctorate in math.) When Larsen was 3 years old, Lindenstrauss recalls, he started asking her philosophical questions about the nature of infinity. “I thought, this kid has a mathematical mind,” said Lindenstrauss, a professor at Indiana University.

    Then a few years ago—around the time that he was immersed in his spelling and crossword projects—he came across a documentary about Yitang Zhang, an unknown mathematician who rose from obscurity in 2013 after proving a landmark result that put an upper bound on the gaps between consecutive prime numbers. Something clicked in Larsen. He couldn’t stop thinking about number theory, and about the related problem that Zhang and other mathematicians still hoped to solve: the twin primes conjecture, which states that there are infinitely many pairs of primes that differ by only 2.


    The High Schooler Who Solved a Prime Number Theorem. Daniel Larsen wouldn’t let go of an old question about Carmichael numbers. “It was just stubbornness on my part,” he said.

    After Zhang’s work, which showed that there are infinitely many pairs of primes that differ by less than 70 million, others jumped in to lower this bound even further. Within months, the mathematicians James Maynard and Terence Tao independently proved an even stronger statement about the gaps between primes. That gap has since shrunk to 246.

    Larsen wanted to understand some of the mathematics underlying Maynard and Tao’s work, “but it was pretty much impossible for me,” he said. Their papers were far too complicated. Larsen tried to read related work, only to find it impenetrable as well. He kept at it, jumping from one result to another, until finally, in February 2021, he came across a paper he found both beautiful and comprehensible. Its subject: Carmichael numbers, those strange composite numbers that could sometimes pass themselves off as prime.

    All but Prime

    In the mid-17th century, the French mathematician Pierre de Fermat wrote a letter to his friend and confidant Frénicle de Bessy, in which he stated what would later be known as his “little theorem.” If N is a prime number, then b^N – b is always a multiple of N, no matter what b is. For instance, 7 is a prime number, and as a result, 2^7 – 2 (which equals 126) is a multiple of 7. Similarly, 3^7 – 3 is a multiple of 7, and so on.

    Mathematicians saw the potential for a perfect test of whether a given number is prime or composite. They knew that if N is prime, b^N – b is always a multiple of N. What if the reverse was also true? That is, if b^N – b is a multiple of N for all values of b, must N be prime?

    Alas, it turned out that in very rare cases, N can satisfy this condition and still be composite. The smallest such number is 561: For any integer b, b^561 – b is always a multiple of 561, even though 561 is not prime. Numbers like these were named after the mathematician Robert Carmichael, who is often credited with publishing the first example in 1910 (though the Czech mathematician Václav Šimerka independently discovered examples in 1885).

    Mathematicians wanted to better understand these numbers that so closely resemble the most fundamental objects in number theory, the primes. It turned out that in 1899—a decade before Carmichael’s result—another mathematician, Alwin Korselt, had come up with an equivalent definition. He simply hadn’t known if there were any numbers that fit the bill.

    According to Korselt’s criterion, a number N is a Carmichael number if and only if it satisfies three properties. First, it must have more than one prime factor. Second, no prime factor can repeat. And third, for every prime p that divides N, p – 1 also divides N – 1. Consider again the number 561. It’s equal to 3 × 11 × 17, so it clearly satisfies the first two properties in Korselt’s list. To show the last property, subtract 1 from each prime factor to get 2, 10 and 16. In addition, subtract 1 from 561. All three of the smaller numbers are divisors of 560. The number 561 is therefore a Carmichael number.

    Though mathematicians suspected that there are infinitely many Carmichael numbers, there are relatively few compared to the primes, which made them difficult to pin down. Then in 1994, Red Alford, Andrew Granville, and Carl Pomerance published a breakthrough paper [below] in which they finally proved that there are indeed infinitely many of these pseudoprimes.

    Unfortunately, the techniques they developed didn’t allow them to say anything about what those Carmichael numbers looked like. Did they appear in clusters along the number line, with large gaps in between? Or could you always find a Carmichael number in a short interval? “You’d think if you can prove there’s infinitely many of them,” Granville said, “surely you should be able to prove that there are no big gaps between them, that they should be relatively well spaced out.”

    In particular, he and his coauthors hoped to prove a statement that reflected this idea—that given a sufficiently large number X, there will always be a Carmichael number between X and 2X. “It’s another way of expressing how ubiquitous they are,” said Jon Grantham, a mathematician at the Institute for Defense Analyses who has done related work.

    But for decades, no one could prove it. The techniques developed by Alford, Granville and Pomerance “allowed us to show that there were going to be many Carmichael numbers,” Pomerance said, “but didn’t really allow us to have a whole lot of control about where they’d be.”

    Then, in November 2021, Granville opened up an email from Larsen, then 17 years old and in his senior year of high school. A paper [below] was attached—and to Granville’s surprise, it looked correct. “It wasn’t the easiest read ever,” he said. “But when I read it, it was quite clear that he wasn’t messing around. He had brilliant ideas.”

    Pomerance, who read a later version of the work, agreed. “His proof is really quite advanced,” he said. “It would be a paper that any mathematician would be really proud to have written. And here’s a high school kid writing it.”

    The key to Larsen’s proof was the work that had drawn him to Carmichael numbers in the first place: the results by Maynard and Tao on prime gaps.

    Unlikely—Not Impossible

    When Larsen first set out to show that you can always find a Carmichael number in a short interval, “it seemed that it was so obviously true, how hard can it be to prove?” he said. He quickly realized it could be very hard indeed. “This is a problem which tests the technology of our time,” he said.

    In their 1994 paper, Alford, Granville, and Pomerance had shown how to create infinitely many Carmichael numbers. But they hadn’t been able to control the size of the primes they used to construct them. That’s what Larsen would need to do to build Carmichael numbers that were relatively close in size. The difficulty of the problem worried his father, Michael Larsen. “I didn’t think it was impossible, but I thought it was unlikely he’d succeed,” he said. “I saw how much time he was spending on it … and I felt it would be devastating for him to give so much of himself to this and not get it.”

    Still, he knew better than to try to dissuade his son. “When Daniel commits to something that really interests him, he sticks with it through thick and thin,” he said.

    So Larsen returned to Maynard’s papers—in particular, to work showing that if you take certain sequences of enough numbers, some subset of those numbers must be prime. Larsen modified Maynard’s techniques to combine them with the methods used by Alford, Granville, and Pomerance. This allowed him to ensure that the primes he ended up with would vary in size—enough to produce Carmichael numbers that would fall within the intervals he wanted.

    “He has more control over things than we’ve ever had,” Granville said. And he achieved this through a particularly clever use of Maynard’s work. “It’s not easy … to use this progress on short gaps between primes,” said Kaisa Matomäki, a mathematician at the University of Turku in Finland. “It’s quite nice that he’s able to combine it with this question about the Carmichael numbers.”

    In fact, Larsen’s argument didn’t just allow him to show that a Carmichael number must always appear between X and 2X. His proof works for much smaller intervals as well. Mathematicians now hope it will also help reveal other aspects of the behavior of these strange numbers. “It’s a different idea,” said Thomas Wright, a mathematician at Wofford College in South Carolina who works on pseudoprimes. “It changes a lot of things about how we might prove things about Carmichael numbers.”

    Grantham agreed. “Now you can do things you never thought of,” he said.

    Larsen, meanwhile, just started his freshman year at the Massachusetts Institute of Technology. He’s not sure what problem he might work on next, but he’s eager to learn what’s out there. “I’m just taking courses … and trying to be open-minded,” he said.

    “He did all this without an undergraduate education,” Grantham said. “I can only imagine what he’s going to be coming up with in graduate school.”

    Science papers:
    breakthrough paper 1994
    A paper 2021

    See the full article here .

    Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct. Use “Reply”.

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  • richardmitnick 10:48 am on January 1, 2023 Permalink | Reply
    Tags: "Hack-and-squirt", "The Secret Life of Plant Killers", , , , To take out invasives the US relies on crews wielding hatchets and chainsaws and herbicide. It’s a messy and fun job—but it may not be enough to stop the spread., WIRED   

    From WIRED: “The Secret Life of Plant Killers” 

    From WIRED

    12.22.22
    Sonya Bennett-Brandt

    1
    Photograph: Kennedi Carter.

    To take out invasives, the US relies on crews wielding hatchets, chainsaws, and herbicide. It’s a messy, fun job—but it may not be enough to stop the spread.

    “When you hunt the “tree of heaven”, you come to know it by its smell. A waft of creamy peanut butter leads you to a tall trunk, silvery and nubbled like cantaloupe rind, rising into a wide crown of papery pink seeds and slender leaves. To kill this tree, you cannot simply cut it down with a chainsaw. Ailanthus altissima is a hydra; it counters any assault by sealing off its wounds and sending up a horde of new shoots across its root system. Where you had one tree, now you have a grove of clones extending 25 feet all around you. No, the trick to killing this tree, Triston Kersenbrock explained, is to attack it “without alarming it,” so slowly that it does not even realize it’s dying.

    Triston and I were standing in the shade of a tree of heaven in Pisgah National Forest, on the fringes of the Appalachian Mountains. We were with his crew of four AmeriCorps members, enjoying a respite from the hot North Carolina summer sun. To my unstudied eye, the tree looked like just another beautiful inhabitant of the ecosystem—and in its native East Asia, that’s what it would be. But here, the species grows so quickly that it takes over the forest canopy, stealing sunlight from the trees, shrubs, and grasses that live below. Its leaves are toxic; when they fall, they poison the soil and suppress the germination of any plant that tries to survive in its shadow.

    The crew members, all in their early to mid-twenties, were on a mission to find and kill as many invasive plants as they could. They were outfitted with identical PPE—long pants and sleeves, turquoise nitrile gloves, safety glasses, and hard hats bearing the logo of their employer, American Conservation Experience, a nonprofit that coordinates environmental restoration work around the country. But each member of the ACE crew retained a personalized style: Triston was neatly ironed and tucked in, a carabiner tidily clipping his car keys to his belt loop. Eva Tillett had tied her pants up with a length of tattered white rope. Carly Coffman hung her safety glasses from a cheerful rainbow-colored strap. Lucas Durham had threaded earbuds through his shirt and under the straps of his helmet so he could listen to jams while he worked. 

    To kill the tree, the ACErs would use a technique known as “hack-and-squirt”. Triston held up a hatchet. “Would you like the honors?” he asked me. I felt a pang. I steadied myself and cut 10 shallow notches into the trunk—minor enough wounds, we hoped, that the tree wouldn’t go into hydra mode. The bark curled off like half-peeled scabs. Eva passed me a squirt bottle full of bright blue liquid containing Triclopyr, an herbicide. “Spritz it, yo!” Lucas said. I spritzed. The liquid filled each wound and dripped down like alien blood. 

    Hack-and-squirt allows the Triclopyr to stealthily infiltrate the tree’s vascular system. The tree, oblivious, carries the poison to its roots, where the chemical mimics one of its own growth hormones and forces its cells to divide themselves to death. Like something out of a Greek myth, the punishment parallels the crime.

    Our work on the big tree took just a few minutes. Then the crew fanned out and went after its offspring. The saplings were too young to have bark, so instead of notching them we shaved a bit of stem off with our hatchet blades and dabbed herbicide into the scrape like antiseptic on a skinned knee. Triston found a sapling that another crew had already tried to kill. It had been cut down to a few knotty stumps, but a bundle of tenacious shoots was erupting out of it. “It doesn’t want to die,” Triston said. We unceremoniously skinned and squirted it. Maybe this time the herbicide would take. 

    Almost 20 years ago, around when American Conservation Experience was founded, the US Forest Service estimated that invasive plants covered 133 million acres in the country, an area as big as California and New York combined. Every year since then, they have claimed millions of additional acres in the United States, incurring billions of dollars in crop losses and land management costs and introducing numerous new pathogens and pests. (The tree of heaven, for example, is the primary reproductive host for the infamous spotted lanternfly, which managed to infest New York City within two years of appearing there.)

    At a time when Earth’s ecosystems are under constant assault from habitat destruction and climate change, invasive plants present a uniquely unsettling global threat. Like Triclopyr, they kill silently and slowly. First they choke out native flora, which means some native herbivores and pollinators start to go hungry, which means some native carnivores do too. Eventually, those species may depart or die out, draining the landscape of biodiversity. The rich, layered variety of the ecosystem gives way to a bland monoculture. Some evolutionary biologists warn of a dawning Homogocene, an era in which invasive species become increasingly dominant—and uniform—across the globe.

    Triston and the ACE crew were here, hacking and hollering, to fight one tiny part of that global advance. They would measure their success not in millions of acres or billions of dollars but in freshly sawn bittersweet stumps, withered spiraea tendrils, and native seedlings winding toward the light. 

    By 7 pm, we were all starving. Dinner was at the sprawling, ranch-style crew house in Asheville where Triston, Eva, Carly, and Lucas lived with an ever-rotating gang of ACEers. The vibe was a combination of college dorm, co-op, and barrack; there were bunk beds, comfy mismatched sofas, and a cherished collection of Star Trek videotapes. 

    When I arrived, Ron Bethea, 25, was choosing a garnish for a shakshuka he’d made with Carly. He picked out a few herbs from an old lunch box crammed with spice blends he collects from every new city he visits. Ron, I learn, is a bit of an ACE legend. A born-and-raised North Carolinian with a sharp sense of humor, he keeps crews entertained with horror stories about rogue birders. (“Birders do not play. They get violent.”) Ron started as an ACE crew member in 2019, became a crew leader in 2020, and was recently promoted to project manager. He watches out for the younger crew members, gently reminding new recruits to brush their teeth. The seemingly endless grind of fieldwork can be a shock, but Ron brings out the fun and drama in the job; when you’re working with Ron, you’re not just weeding, you’re waging war. “I don’t know if you’ve seen anyone play Call of Duty, but that’s exactly how it feels,” Ron said. “We have our ammunition, we’re coordinating our strategies. Like ‘Hey, you go around this tree line, I’ll go around the other side, and we’ll meet you in the middle.’”

    “He’s a great cook,” Lucas told me. “He’s so iconic.” Carly pulled out her water bottle and showed me a sticker of Ron in his trademark tie-dye bandana. Wreathing his head was one of his catchphrases: “It be ya own bitches.” As in, trust no one. 

    2
    Ron Bethea, an ACE project manager. Photograph: Kennedi Carter.

    The six of us sat down at a big scuffed-up table, surrounded by crew members’ handmade artwork and goofy photos tacked to the walls. Over dinner, while we passed around Ron’s garlic confit, everyone told their funniest stories from the summer. Like how once Ron ugly-cried after accidentally chainsawing in half a turtle that was hidden in an old log. There was the time a crew member peed on a hornet’s nest and sicced the hornets on the rest of the crew; the only person to escape unscathed had his oversize T-shirt to thank. “He was built like a toothpick in a garbage bag!” Ron said—the stingers just couldn’t find him. Another time, an angry wasp flew down a crew member’s shirt, but he stayed so calm no one believed him. “I’m being stung. Ow. I’m being stung,” he’d said, serenely. 

    The crew’s easy camaraderie had formed over just a few months. ACE functions as a contractor for government organizations that need conservation work done, including the Park Service, the Forest Service, Fish and Wildlife, the Bureau of Land Management, and municipalities. Its funding is pieced together from federal agencies, grants, and other nonprofits, like the Conservation Fund or the Nature Conservancy. For labor, the organization relies on training inexperienced young people to be, essentially, short-term volunteers; besides room and board, crew members receive a living allowance of $240 per week. You don’t need a college degree to serve in AmeriCorps, and the program grants an education award that can be applied to tuition or student loans. It gives aspiring conservationists a chance to build land and forest management expertise that can only come from being in the field. 

    Everyone around the table was there for different reasons. Triston hoped the field experience would help him get a long-term job with the Forest Service. Carly was shadowing Triston. Lucas was looking for something interesting to do during his summer break from college. Eva had a degree in ecology and was hoping to leave her office job for something more hands-on. Many ACEers are trying to jump-start conservation careers; others just want to work in nature for a while. Some stay for a few months; a few, like Ron, stay for years. 

    In his time at ACE, Ron has worked on invasive plant removal projects across the East Coast and all the way to Kansas; he’s traveled to seven states this year alone. Over his tenure, he’s grown to appreciate the wiliness of his floral foes. “These plants are smart. They know what they’re doing,” Ron told me. “They’re invasive because they know.”

    Out of all the non-native plants that arrive in North America, only a fraction become invasive. Most either perish immediately or weave themselves into their new ecosystems, participating in the normal push and pull of predation, symbiosis, and competition. But even a small number of invasive species can quickly provoke disaster because they share traits that make them impressively resilient: They are hyper-fertile and fast-growing, with an arsenal of botanical superpowers that allow them to decimate native flora and transform their surroundings according to their own tastes.

    Climate change is only accelerating the problem. Across the country, growing seasons for invasive plants are getting longer. In the Southeast, winter freezes were once an effective natural weapon against tropical plants that tried to grow in the temperate ecosystem. Now, as the region warms, the plants can survive year-round.

    3
    Ron Bethea collects specimens of invasive plants in jars. Photograph: Kennedi Carter.

    It’s worth noting that most invasive plants aren’t true invaders; they are escape artists. Every one of the invasive plants I saw in North Carolina was brought to North America deliberately in the 18th and 19th centuries, during a kind of horticultural free-for-all. Wealthy enthusiasts scooped up attractive plants from across the world and promoted them as exotic, hardy additions to gardens, parks, and hedgerows. Then, one by one, the plants escaped from cultivation, and these luxury goods transformed into ecological disasters. Some of America’s most noxious invasive plants—floating heart, Asiatic bittersweet, Japanese meadowsweets, princess tree, porcelain berry—are the botanical pets of aristocrats, gone feral. 

    The sun was about to rise when I joined Ron and an ACE wetland restoration crew in Raleigh’s Walnut Creek Wetland Park for the start of their work day. The park preserves a corner of wilderness within one of the city’s lowest-income areas. For decades, the nearby creek was a dumping ground for sewage. Local residents started doing volunteer cleanups, and in the 90s funding was secured to create the park. This was a big win for biodiversity; wetland ecosystems like the park support more than 70 percent of North Carolina’s protected species. Now, the park is being eaten by kudzu, and this crew was tasked with removing it. 

    Kudzu, the infamous “vine that ate the South,” lives up to the hype. Most of the roadsides I saw in North Carolina had been fully digested into a surreal kudzu-textured world. Tree-shaped kudzu. A delicate curve of telephone-wire-shaped kudzu. Barn-shaped kudzu, with little kudzu chimneys. “If you leave for six months, your car belongs to the wilderness,” Ron said. “It’s not your car anymore.” The vine can grow a foot a day.

    Invasive vines tend to be serial stranglers. Not only do they climb high enough to cover the canopy and steal sunlight, they can wrap trees so tightly that they squeeze the sapwood, making it harder for water and nutrients to travel between the canopy and the roots. It’s yet another ability that allows invasive vines to outcompete their native counterparts. On the bright side, it makes them easier for an inexperienced invasive-plant hunter like myself to identify. Just keep an eye out for the stranglers, one ACE project manager told me. “Native vines that are meant to be here don’t girdle trees just for fun.” 

    4
    Ron looks at a growth of Oriental bittersweet. Photograph: Kennedi Carter.

    Ron and Emery Harms, the crew leader, drove me and the crew into the park to get us closer to the day’s first target site, and we armed ourselves with hand tools from a fat plastic bucket: thick gardening gloves, handsaws that unfolded like switchblades, loppers, and squeeze bottles with spongy tips for blotting herbicide. Thus equipped, we began the kudzu massacre. Whenever the crew and I painstakingly unwound a kudzu vine from the tree beneath, it left craggy scars in the bark. Slowly, native white ash and Eastern cottonwood trees appeared from below the kudzu, like freed hostages. Then, to make sure the vines didn’t just climb right back up, we had to find and chop the root—or rather, roots, because a single vine can have several root sites. It was like untangling a colossal, fragile knot, except every mistake generated a new knot. More than once, I pulled on the end of a kudzu vine, chasing the stem up and down trees and under old logs—only to find one of my crewmates pulling on the other end, like a giant, botanical version of the spaghetti scene from Lady and the Tramp. Meanwhile, every tug on a vine covered us in kudzu bugs: chunky, invasive sap-suckers that pinged off our safety helmets like hail. 

    The wetland itself was lush and lively with animals, with a warm buzz of crickets, grasshoppers, and frogs. After a few hours, one of the crew members called everyone over and we stopped working for a moment to watch a wolf spider carrying her egg sac, a perfect blue marble, through the grass.

    5
    Ron holds up a salt cedar specimen. Photograph: Kennedi Carter.

    In the afternoon, we tackled a clump of wetland where kudzu, bittersweet, and invasive privet shrubs wrapped thickly together into an evil matrix. We were “windowing”: creating an open space between the bottom of the canopy and the ground to remove the invasive vines’ access to soil and bring sunlight back to the forest floor. While Emery tackled the nearly foot-thick privet trunk with a chainsaw, I kept carefully outside the “blood bubble”—the hypothetical circle circumscribed by an outstretched arm holding a chainsaw—and hacked away at a smaller shrub with a handsaw. Once Emery cut completely through the trunk, I braced for the tree to fall, but instead it hung in the air like a ghost, its whole weight suspended from above by the vines knotted around its canopy. We cheered as Ron dragged the tree, 10 times his size, to the deadwood pile. By the end of the afternoon, we’d turned the shady thicket, clotted with privet, into a sunny, airy clearing. “It seems like you’ve got a bloodlust now,” Emery said to me. 

    In that new clearing, native plants will have a chance to gain back a little ground. Other parts of the park are too far gone. As we walked back to the ACE van at the end of the day, Emery pointed out a monster tower of kudzu, too dense to chop; “I’d have loved to hit that,” they said wistfully, “but it would have grown back in three weeks.” With limited manpower, crews have to ruthlessly prioritize areas where they can have the most impact. The goal is to do enough to keep native plants in the game until their next visit. As Ron put it, “it’s never a one-and-done deal.” Even in the best-case scenario, the same fight will keep playing out season after season. “On the one hand, it looks better than it was,” one crew member said. “But compared to what it could be … woof.” In this field, every victory is a small win. If the birds, amphibians, insects, and other creatures that rely on the wetland can flourish for another year, that will have to do. 

    6
    A hack-and-squirt treatment (L) and treatment on a tree of heaven stump (R). Photograph: Kennedi Carter.

    Is the painstaking, piecemeal work of halting invasives more trouble than it’s worth? Some ecologists argue that if the plants are left alone, the ecosystems will manage themselves. Invasive species, the thinking goes, will eventually become less dominant as they build connections to other organisms and as those other organisms evolve defenses against them. Given some time, native species can put up a fight against the Homogocene. When I asked Joost Besijn, the director of ACE’s eastern division, about this idea, he said that in the long term it could prove true—but in many cases, “long” might be longer than people can afford. “I guess it all depends on the time scale you look at,” he said. “In a million years, does it really matter? But in the short term, many invasive species will completely decimate the carrying capacity of an ecosystem.”

    In the face of such enormous and intractable environmental problems, the public tends to look to the white-collar experts—scientists, researchers, policymakers—for answers. But in North Carolina, I saw that some of the United States’ most immediate needs depend on an entirely different set of skills. The truth is that once invasive vegetation takes hold, the only viable mitigation strategy is to send in crews of people—mostly young, underpaid people on temporary contracts—to wield hatchets, chainsaws, and herbicide in the tangle of the forest, taking out plants one at a time.

    ACE’s conservation corps model has its appeal. The chaotic gaggle of young people in Triston’s and Emery’s crews transmitted an infectious energy. They showed me which plants had serrated leaves or backward-hooked thorns and hairs on their stems. They taught me which plants smelled like root beer and Froot Loops. When we walked alone into the forest, we stayed within “whooping distance” of each other; every so often a “WHOOP!” or a “YEE!” would drift through the trees and we would each hoot back our locations. I sneezed, and someone shouted “BLESS YOU!” from far away. When our hands were too grubby to accept a stick of gum, Eva went around and placed a piece in each of our mouths like a communion wafer.

    7
    Ron and another ACE worker sharpen loppers on a truck tailgate. Photograph: Kennedi Carter.

    The care each crew leader had for their members was plain. Emery checked on everyone’s bug bites and always knew which crew members had leaky boots. Triston took on all the hardest jobs himself. Ron handed around his contact info in case anyone ever needed a job reference or a pep talk. Several crew members talked to me about the new skills they were learning, even beyond the field of conservation: budgeting, teamwork, harmonious co-living.

    Camaraderie, though, may not be enough to sustain a vital front of conservation work. Most of the people I spoke with who do plant removal feared long-term financial struggle. Full-time, hands-on positions in conservation generally require field experience, which is often unpaid. One route to a viable career is the Forest Service, but much of that work is seasonal. Some people work second jobs; others depend on savings. Ron would like to go back to school to get an advanced degree, but he’s hesitant. “I need to get on that train, but I am in debt too bad,” he told me. “I just need to breathe for a minute.” ACE’s most significant challenge right now isn’t finding funders—it’s finding enough members willing to do the work.

    Recently, ACE leadership, alongside other conservation corps from across the country, took part in conversations in DC about how to replace volunteer or poorly paid labor with a paid conservation workforce. In Ron’s estimation, even a wage of $15 an hour, plus benefits, “would change ACE entirely.” But President Joe Biden’s infrastructure bill was passed with only about $250 million set aside for an invasive plant elimination program. That’s not a lot of money to tackle one of the country’s biggest biodiversity threats. 

    As it stands, invasive plants are gaining ground in the vast majority of the country’s natural areas. Once I started seeing them, I couldn’t stop—since my visit to North Carolina, I spotted a baby kudzu twisting up a tree in a city park, hogweed on a hiking trail, garlic mustard in parking lots, a spiraea bush behind a taco shop. They have us surrounded. Check your backyard, and your local park; maybe they’re there, strangling trees or casting a deadly shade. If you’re lucky, a troop of young conservationists will stop by, when funding allows, to give native plants and wildlife a fighting chance for another season. 

    Driving out of Pisgah National Forest after a long day of cut-stumping, stump-squirting, trunk-hacking, and vine-pulling, the ACE crew spotted a massive bank of bittersweet on the roadside, choking a telephone pole. The vine was only a few months away from reaching the top and winding along the wires like a Christmas garland. “Don’t look!” someone squealed, and we all covered our eyes.”

    See the full article here .

    Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct. Use “Reply”.

    five-ways-keep-your-child-safe-school-shootings

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  • richardmitnick 9:22 am on December 26, 2022 Permalink | Reply
    Tags: "A New Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations", "Proof by Computer", A 177-page proof — the result of a decade-long research program — makes significant use of computers., A million-dollar Millennium Prize awaits anyone who can prove whether similar failures occur in the Navier-Stokes equations-a generalization of the Euler equations that accounts for viscosity., Euler equations, For centuries mathematicians have sought to understand and model the motion of fluids., In fluid mechanics computer-assisted proofs are still a relatively new technique., It gets even more complicated if you’re trying to model a fluid that has viscosity-as almost all real-world fluids do., It’s impossible for a computer to calculate infinite values. It can get very close to seeing a singularity but it can’t actually reach it, Mathematicians want to establish whether equations that model fluid flow can sometimes fail or “blow up.”, , Navier-Stokes equations, The "Move to Self-Similar Land", The motion of fluids, These efforts mark a growing trend in the field of fluid dynamics: the use of computers to solve important problems., WIRED   

    From “Quanta Magazine” : “A New Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations” 

    From “Quanta Magazine”

    11.16.22 [Just found this via Wired
    Jordana Cepelewicz

    1
    Mathematicians want to establish whether equations that model fluid flow can sometimes fail, or “blow up.” Quanta Magazine


    Mathematicians want to establish whether equations that model fluid flow can sometimes fail, or “blow up.” Credit: DVDP for Quanta Magazine.

    For centuries mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the weather, design better airplanes, and characterize how blood flows through the circulatory system. These equations are deceptively simple when written in the right mathematical language. However, their solutions are so complex that making sense of even basic questions about them can be prohibitively difficult.

    Perhaps the oldest and most prominent of these equations, formulated by Leonhard Euler more than 250 years ago, describe the flow of an ideal, incompressible fluid: a fluid with no viscosity, or internal friction, that cannot be forced into a smaller volume. “Almost all nonlinear fluid equations are kind of derived from the Euler equations,” said Tarek Elgindi, a mathematician at Duke University. “They’re the first ones, you could say.”

    Yet much remains unknown about the Euler equations — including whether they’re always an accurate model of ideal fluid flow. One of the central problems in fluid dynamics is to figure out if the equations ever fail, outputting nonsensical values that render them unable to predict a fluid’s future states.

    Mathematicians have long suspected that there exist initial conditions that cause the equations to break down. But they haven’t been able to prove it.

    In a new science paper [below] posted online last month, a pair of mathematicians has shown that a particular version of the Euler equations does indeed sometimes fail. The proof marks a major breakthrough — and while it doesn’t completely solve the problem for the more general version of the equations, it offers hope that such a solution is finally within reach. “It’s an amazing result,” said Tristan Buckmaster, a mathematician at the University of Maryland who was not involved in the work. “There are no results of its kind in the literature.”

    There’s just one catch.

    The 177-page proof — the result of a decade-long research program — makes significant use of computers. This arguably makes it difficult for other mathematicians to verify it. (In fact, they are still in the process of doing so, though many experts believe the new work will turn out to be correct.) It also forces them to reckon with philosophical questions about what a “proof” is, and what it will mean if the only viable way to solve such important questions going forward is with the help of computers.

    Sighting the Beast

    In principle, if you know the location and velocity of each particle in a fluid, the Euler equations should be able to predict how the fluid will evolve for all time. But mathematicians want to know if that’s actually the case. Perhaps in some situations, the equations will proceed as expected, producing precise values for the state of the fluid at any given moment, only for one of those values to suddenly skyrocket to infinity. At that point, the Euler equations are said to give rise to a “singularity” — or, more dramatically, to “blow up.”

    Once they hit that singularity, the equations will no longer be able to compute the fluid’s flow. But “as of a few years ago, what people were able to do fell very, very far short of [proving blowup],” said Charlie Fefferman, a mathematician at Princeton University.

    It gets even more complicated if you’re trying to model a fluid that has viscosity (as almost all real-world fluids do). A million-dollar Millennium Prize from the Clay Mathematics Institute awaits anyone who can prove whether similar failures occur in the Navier-Stokes equations, a generalization of the Euler equations that accounts for viscosity.

    In 2013, Thomas Hou, a mathematician at the California Institute of Technology, and Guo Luo, now at the Hang Seng University of Hong Kong, proposed a scenario in which the Euler equations would lead to a singularity. They developed a computer simulation of a fluid in a cylinder whose top half swirled clockwise while its bottom half swirled counterclockwise. As they ran the simulation, more complicated currents started to move up and down. That, in turn, led to strange behavior along the boundary of the cylinder where opposing flows met. The fluid’s vorticity — a measure of rotation — grew so fast that it seemed poised to blow up.

    2
    Merrill Sherman/Quanta Magazine.

    Hou and Luo’s work was suggestive, but not a true proof. That’s because it’s impossible for a computer to calculate infinite values. It can get very close to seeing a singularity, but it can’t actually reach it — meaning that the solution might be very accurate, but it’s still an approximation. Without the backing of a mathematical proof, the value of the vorticity might only seem to be increasing to infinity because of some artifact of the simulation. The solutions might instead grow to enormous numbers before again subsiding.

    Such reversals had happened before: A simulation would indicate that a value in the equations blew up, only for more sophisticated computational methods to show otherwise. “These problems are so delicate that the road is littered with the wreckage of previous simulations,” Fefferman said. In fact, that’s how Hou got his start in this area: Several of his earlier results disproved the formation of hypothetical singularities.

    Still, when he and Luo published their solution, most mathematicians thought it was very likely a true singularity. “It was very meticulous, very precise,” said Vladimir Sverak, a mathematician at the University of Minnesota. “They really went to great lengths to establish that this is a real scenario.” Subsequent work by Elgindi, Sverak and others only strengthened that conviction.

    But a proof was elusive. “You’ve sighted the beast,” Fefferman said. “Then you try to capture it.” That meant showing that the approximate solution that Hou and Luo so carefully simulated is, in a specific mathematical sense, very, very close to an exact solution of the equations.

    Now, nine years after that first sighting, Hou and his former graduate student Jiajie Chen have finally succeeded in proving the existence of that nearby singularity.

    The Move to Self-Similar Land

    Hou, later joined by Chen, took advantage of the fact that, upon closer analysis, the approximate solution from 2013 seemed to have a special structure. As the equations evolved through time, the solution displayed what’s called a self-similar pattern: Its shape later on looked a lot like its earlier shape, only re-scaled in a specific way.

    As a result, the mathematicians didn’t need to try to look at the singularity itself. Instead, they could study it indirectly by focusing on an earlier point in time. By zooming in on that part of the solution at the right rate — determined based on the solution’s self-similar structure — they could model what would happen later on, including at the singularity itself.

    It took a few years for them to find a self-similar analogue to the 2013 blowup scenario. (Earlier this year, another team of mathematicians, which included Buckmaster, used different methods to find a similar approximate solution. They are currently using that solution to develop an independent proof of singularity formation.)

    With an approximate self-similar solution in hand, Hou and Chen needed to show that an exact solution exists nearby. Mathematically, this is equivalent to proving that their approximate self-similar solution is stable — that even if you were to slightly perturb it and then evolve the equations starting at those perturbed values, there’d be no way to escape a small neighborhood around the approximate solution. “It’s like a black hole,” Hou said. “If you start with a profile close by, you’ll be sucked in.”

    But having a general strategy was just one step toward the solution. “Fussy details matter,” Fefferman said. As Hou and Chen spent the next several years working out those details, they found that they had to rely on computers once again — but this time in an entirely new way.

    A Hybrid Approach

    Among their first challenges was figuring out the exact statement they had to prove. They wanted to show that if they took any set of values close to their approximate solution and plugged it into the equations, the output wouldn’t be able to stray far. But what does it mean for an input to be “close” to the approximate solution? They had to specify this in a mathematical statement — but there are many ways to define the notion of distance in this context. For their proof to work, they needed to choose the correct one.

    “It has to measure different physical effects,” said Rafael de la Llave, a mathematician at the Georgia Institute of Technology. “So it needs to be chosen using a deep understanding of the problem.”

    Once they had the right way to describe “closeness,” Hou and Chen had to prove the statement, which boiled down to a complicated inequality involving terms from both the re-scaled equations and the approximate solution. The mathematicians had to make sure that the values of all those terms balanced out to something very small: If one value ended up being large, other values had to be negative or kept in check.

    “If you make something a little too big or a little too small, the whole thing breaks down,” said Javier Gómez-Serrano, a mathematician at Brown University. “So it’s very, very careful, delicate work.”

    “It’s a really fierce fight,” Elgindi added.

    To get the tight bounds they needed on all these different terms, Hou and Chen broke the inequality into two major parts. They could take care of the first part by hand, with techniques including one that dates back to the 18th century, when the French mathematician Gaspard Monge sought an optimal way of transporting soil to build fortifications for Napoleon’s army. “Stuff like this has been done before, but I found it striking that [Hou and Chen] used it for this,” Fefferman said.

    That left the second part of the inequality. Tackling it would require computer assistance. For starters, there were so many calculations that needed to be done, and so much precision required, that “the amount of work you’d have to do with pencil and paper would be staggering,” de la Llave said. To get various terms to balance out, the mathematicians had to perform a series of optimization problems that are relatively easy for computers but exceedingly time-consuming for humans. Some of the values also depended on quantities from the approximate solution; since that was calculated using a computer, it was more straightforward to also use a computer to perform these additional computations.

    “If you try to manually do some of these estimates, you’re probably going to overestimate at some point, and then you lose,” said Gómez-Serrano. “The numbers are so tiny and tight … and the margin is incredibly thin.”

    But because computers can’t manipulate an infinite number of digits, tiny errors inevitably occur. Hou and Chen had to carefully track those errors, to make sure they didn’t interfere with the rest of the balancing act.

    Ultimately, they were able to find bounds for all the terms, completing the proof: The equations had indeed produced a singularity.

    Proof by Computer

    It remains open whether more complicated equations — the Euler equations without the presence of a cylindrical boundary and the Navier-Stokes equations — can develop a singularity. “But [this work] at least gives me hope,” Hou said. “I see a path forward, a way to maybe even eventually resolve the full Millennium problem.”

    Meanwhile, Buckmaster and Gómez-Serrano are working on a computer-assisted proof of their own — one they hope will be more general, and therefore capable of tackling not just the problem that Hou and Chen solved, but also scores of others.

    These efforts mark a growing trend in the field of fluid dynamics: the use of computers to solve important problems.

    “In a number of different areas of mathematics, it’s occurring more and more frequently,” said Susan Friedlander, a mathematician at the University of Southern California.

    But in fluid mechanics computer-assisted proofs are still a relatively new technique. In fact, when it comes to statements about singularity formation, Hou and Chen’s proof is the first of its kind: Previous computer-assisted proofs were only able to tackle toy problems in the area.

    Such proofs aren’t so much controversial as “a matter of taste,” said Peter Constantin of Princeton University. Mathematicians generally agree that a proof has to convince other mathematicians that some line of reasoning is correct. But, many argue, it should also improve their understanding of why a particular statement is true, rather than simply provide validation that it’s correct. “Do we learn anything fundamentally new, or do we just know the answer to the question?” Elgindi said. “If you view mathematics as an art, then this is not so aesthetically pleasing.”

    “A computer can help. It’s wonderful. It gives me insight. But it doesn’t give me a full understanding,” Constantin added. “Understanding comes from us.”

    For his part, Elgindi still hopes to work out an alternative proof of blowup entirely by hand. “I’m overall happy this exists,” he said of Hou and Chen’s work. “But I take it as more of a motivation to try to do it in a less computer-dependent way.”

    Other mathematicians view computers as a vital new tool that will make it possible to attack previously intractable problems. “Now the work is no longer just paper and pencil,” Chen said. “You have the option of using something more powerful.”

    According to him and others (including Elgindi, despite his personal preference for writing proofs by hand), there’s a good possibility that the only way to solve big problems in fluid dynamics — that is, problems that involve increasingly complicated equations — might be to rely heavily on computer assistance. “It looks to me as if trying to do this without making heavy use of computer-assisted proofs is like tying one or possibly two hands behind your back,” Fefferman said.

    If that does end up being the case and “you don’t have any choice,” Elgindi said, “then people … such as myself, who would say that this is suboptimal, should be quiet.” That would also mean that more mathematicians would need to start learning the skills needed to write computer-assisted proofs — something that Hou and Chen’s work will hopefully inspire. “I think there were a lot of people who were simply waiting for someone to solve such a problem before investing any of their own time into this approach,” Buckmaster said.

    That said, when it comes to debates about the extent to which mathematicians should rely on computers, “it’s not that you need to pick a side,” Gómez-Serrano said. “[Hou and Chen’s] proof wouldn’t work without the analysis, and the proof wouldn’t work without the computer assistance. … I think the value is that people can speak the two languages.”

    With that, de la Llave said, “there’s a new game in town.”

    Science paper:
    new science paper
    See the science paper for instructive material with images.

    See the full article here .

    Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct. Use “Reply”.

    five-ways-keep-your-child-safe-school-shootings

    Please help promote STEM in your local schools.

    Stem Education Coalition

    Formerly known as Simons Science News, Quanta Magazine is an editorially independent online publication launched by the Simons Foundation to enhance public understanding of science. Why Quanta? Albert Einstein called photons “quanta of light.” Our goal is to “illuminate science.” At Quanta Magazine, scientific accuracy is every bit as important as telling a good story. All of our articles are meticulously researched, reported, edited, copy-edited and fact-checked.

     
  • richardmitnick 10:15 am on December 12, 2022 Permalink | Reply
    Tags: "‘Solar Twins’ Reveal the Consistency of the Universe", , Attracting protons and electrons to form atoms—which then bind into molecules to form almost everything else., “The color of sunlight”: the distinctive properties help reveal the quantum structure of the atoms that make up the stars and all matter around us., , , Does the electromagnetic force behave consistently across the entire universe—or at least among these stars?, , , If the fundamental physics of stars is different when comparing them to each other that would hint that something is wrong with the way we understand cosmology., Much of the gold and platinum and other heavy elements on our planet are forged in the collisions of neutron stars., Physicists study starlight to find whether the fine structure constant-whose value makes our universe possible-really is the same everywhere., , , The color of the light emitted by stars similar to the sun in temperature and size and elemental content—”solar twins”, The team used starlight to measure what’s known as the fine structure constant-a number that sets the strength of the electromagnetic force., WIRED   

    From “WIRED“: “‘Solar Twins’ Reveal the Consistency of the Universe” 

    From “WIRED“

    12.9.22
    Sophia Chen

    Physicists study starlight to find whether the fine structure constant-whose value makes our universe possible-really is the same everywhere.

    1
    Photograph: NASA.

    Sometimes we must look to the heavens to understand our own planet. In the 17th century, Johannes Kepler’s insight that planets move in elliptical orbits around the sun led to a deeper understanding of gravity, the force that determines Earth’s tides. In the 19th century, scientists studied the color of sunlight, whose distinctive properties helped reveal the quantum structure of the atoms that make up the star—and all matter around us. In 2017, the detection of gravitational waves showed that much of the gold and platinum and other heavy elements on our planet are forged in the collisions of neutron stars. 

    Michael Murphy studies stars in this tradition. An astrophysicist at Swinburne University of Technology in Australia, Murphy analyzes the color of the light emitted by stars similar to the sun in temperature and size and elemental content—”solar twins,” as they are called. He wants to know what their properties reveal about the nature of the electromagnetic force, which attracts protons and electrons to form atoms—which then bind into molecules to form almost everything else. 

    In particular, he wants to know if this force behaves consistently across the entire universe—or at least, among these stars. In a recent paper in Science [below], Murphy and his team used starlight to measure what’s known as the fine structure constant, a number that sets the strength of the electromagnetic force. “By comparing the stars to each other, we can learn if their fundamental physics is different,” says Murphy. If it is, that hints that something is wrong with the way we understand cosmology.

    Science paper:
    Science

    See the full article here .

    Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct. Use “Reply”.

    five-ways-keep-your-child-safe-school-shootings

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  • richardmitnick 9:36 am on November 27, 2022 Permalink | Reply
    Tags: "EUC": Equatorial Undercurrent, "The Geological Fluke That's Protecting Sea Life in the Galapagos", , , , , Could it be that the water offshore will become a refuge for marine animals seeking cold water in a warming world? The answer it seems is yes. At least for a while., , , , The cool water sustains populations of penguins; marine iguanas; sea lions; fur seals and cetaceans that would not be able to stay on the equator year round., The Galapagos cold pool is a product of the shape of the seafloor and the rotation of the planet—two things unlikely to change because of rising greenhouse gases., The Galapagos could become a genetic bank that could be used to reseed devastated marine ecosystems elsewhere., The Galapagos Islands are already famed for their biodiversity., The islands are in the line of an icy current that provides marine ecosystems refuge amid warming oceans. But the good news might not last for long., There are other cold pools on the planet. One in the North Atlantic just south of Greenland is caused by the weakening of a global current that carries heat north., This cooling is the product of upwelling caused by the collision of a deep ocean current against the islands lying in its path., WIRED   

    From “WIRED“: “The Geological Fluke That’s Protecting Sea Life in the Galapagos” 

    From “WIRED“

    11.26.22
    Richard Kemeny

    The islands are in the line of an icy current that provides marine ecosystems refuge amid warming oceans. But the good news might not last for long.

    1
    Photograph: Wolfgang Kaehler/Getty Images.

    Pushed by climate change, almost every part of the ocean is heating up. But off the west coast of the Galapagos Islands, there is a patch of cold, nutrient-rich water. This prosperous patch feeds phytoplankton and breathes life into the archipelago.

    “The cool water sustains populations of penguins, marine iguanas, sea lions, fur seals, and cetaceans that would not be able to stay on the equator year round,” says Judith Denkinger, a marine ecologist at the Universidad San Francisco de Quito in Ecuador.

    Over the past four decades, this cold patch has cooled by roughly half a degree. Its persistence has scientists wondering how long it will hold. The Galapagos Islands are already famed for their biodiversity. Could it be that the water offshore will become a refuge for marine animals seeking cold water in a warming world? The answer, it seems, is yes. At least for a while.

    There are other cold pools on the planet. One, in the North Atlantic just south of Greenland, is caused by the weakening of a global current that carries heat north. But according to a new study [Geophysical Research Letters (below)] led by Kris Karnauskas and Donata Giglio, climate scientists at the University of Colorado-Boulder, the Galapagos cold pool is a product of the shape of the seafloor and the rotation of the planet—two things unlikely to change because of rising greenhouse gases. And the Galapagos are not the only islands seeing this effect.

    Along the equator, several islands have unusually cold water lying immediately to their west. According to Karnauskas and Giglio’s work, this cooling is the product of upwelling caused by the collision of a deep ocean current against the islands lying in its path.

    Analyzing 22 years’ worth of ocean temperature data collected by Argo floats, along with observations from satellites, ocean gliders, and cruises, the scientists constructed temperature profiles around several equatorial islands and pinpointed the location of the Equatorial Undercurrent (EUC), a cold, fast-flowing current that travels eastward about 100 meters below the surface of the Pacific Ocean. The EUC is held in place along the equator by the Coriolis force, an inertia brought on by the Earth’s spin on its axis. This same effect twists hurricanes anticlockwise north of the equator and clockwise south of it.

    Karnauskas and Giglio’s work shows that when the EUC gets within 100 kilometers west of the Galapagos Islands, it suddenly intensifies as it’s diverted upward by the islands. This causes the water to be up to 1.5 degrees Celsius cooler than the water outside this cold pool. The researchers found a similar, yet weaker, effect west of the Gilbert Islands in the western Pacific Ocean.

    In a separate study, Karnauskas shows that over the past few decades, the EUC has been getting stronger and deeper. It’s also moved about 10 kilometers south, bringing its path more in line with the Galapagos Islands. All of those changes contribute to the observed cooling, says Karnauskas.

    For the Galapagos marine ecosystem, this cooling is “a bit of a mixed bag,” says Jon Witman, a marine ecologist at Brown University in Rhode Island who was not involved in the studies. “The cool upwelled water of the EUC certainly has important positive impacts,” he says. But when combined with other oceanic processes that also cause temperatures to drop, such as La Niña, the cooling can hurt certain wildlife, such as by cold shocking corals, causing them to bleach and sometimes die.

    For the near future, this shield of cold will likely benefit life around the Galapagos Islands and other equatorial islands. But this cooling water is fighting a losing battle with a warming atmosphere, says Karnauskas. “This cooling trend probably won’t last through the century; it will eventually be overwhelmed,” he says.

    If some species are protected at least for a while, however, the Galapagos could become a genetic bank that could be used to reseed devastated marine ecosystems elsewhere, suggests Karnauskas. “And it’s just beautiful that it’s the iconic Galapagos that we’re talking about here.”

    Science paper:
    Geophysical Research Letters

    See the full article here .

    Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct.

    five-ways-keep-your-child-safe-school-shootings

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  • richardmitnick 10:48 am on October 8, 2022 Permalink | Reply
    Tags: "A Huge New Data Set Pushes the Limits of Neuroscience", , For decades neuroscientists have stuck thin metal electrodes into the brains of mice and finches and monkeys to spy on individual neurons and figure out what sets them off., , Neuroscientists use an approach called “dimensionality reduction” to make visualization possible., Regions like the prefrontal cortex where every neuron responds to a whole host of things seem to operate much more like a workshop in which each artisan has expertise in a wide range of tasks., Scientists ran up against analytical walls when they looked at neurons one-by-one., The challenge now is figuring out just how to parse all that data., WIRED, With the development of Neuropixels probes in 2017 scientists can listen to hundreds of neurons at once.   

    From “WIRED“: “A Huge New Data Set Pushes the Limits of Neuroscience” 

    From “WIRED“

    10.3.22
    Grace Huckins

    The Allen Institute’s release includes recordings from a whopping 300,000 mouse neurons. Now the challenge is figuring out what to do with all that data.

    1
    Illustration: JUAN GAERTNER/Getty Images.

    There’s a video that’s shown in almost every introductory neuroscience course. It doesn’t look like much—a bar of light shifting and rotating across a black screen while the background audio pops and crackles like the sound of a faraway fireworks show. Dry stuff, until you learn that the pops represent the firing of a single neuron in the brain of a cat, who is watching the bar move on the screen. When the bar reaches a specific location and lies at a particular angle, the popping explodes in a grand finale of frantic activity. The message is clear: This neuron really, really cares about that bar.

    The experiment shown in the video was performed by David Hubel and Torsten Wiesel in the 1960s and helped scientists infer basic principles about how the visual system works. For decades since, neuroscientists have stuck thin, metal electrodes into the brains of mice, finches, and monkeys to spy on individual neurons and figure out what sets them off. There are neurons that respond to specific colors or shapes; or to particular locations in space or the direction of one’s head; or to whole faces or individual features.

    As powerful an engine as single-cell analysis has proven, “Everybody always wanted more neurons,” says Anne Churchland, professor of neurobiology at the University of California-Los Angeles. Part of the reason was simple statistics: More observations are always better, no matter the experiment. But scientists also ran up against analytical walls when they looked at neurons one-by-one. In the prefrontal cortex, the region at the front of the brain that plays major roles in planning, decision-making, and social behavior, neurons respond to such a diversity of things—visual features, tasks, decisions—that researchers have been unable to assign them any particular role, at least individually. Even in the primary visual cortex, the area far to the back of the brain where Hubel and Wiesel made their recordings, only a fraction of neurons actually fire when the animal looks at oriented bars [Nature (below)].

    With Hubel and Wiesel’s techniques, looking at more than a handful of neurons at once was impossible. But engineers have pushed and pushed that capacity, culminating in the development of Neuropixels probes in 2017. One centimeter long and made of silicon, a single probe can listen to hundreds of neurons at once and is small enough that neuroscientists can stick several of them into an animal’s brain. At the Allen Institute, a nonprofit research institute started by Microsoft cofounder Paul Allen, they used six Neuropixels probes to record simultaneously from eight different regions of the mouse visual system. In August, the institute released data [Allen Brain Map (below)] from 81 mice—comprising the activity of around 300,000 neurons. The data is freely available to any researchers who might want to use it.

    As the largest data set of this kind ever collected—three times as big as the previous record holder—the release lets researchers observe enormous groups of neurons acting in concert. That unprecedented scale may unlock opportunities to understand parts of cognition that have previously evaded the scientific community’s grasp. “We want to understand how we think and see and make decisions,” says Shawn Olsen, an investigator at the Allen Institute who played a central role in the project. “And it just does not happen at the level of single neurons.”

    The challenge now is figuring out just how to parse all that data. Gargantuan data sets aren’t easy to handle; even sharing and downloading them can be difficult. But as tricky as the analysis may prove, working with such data sets is eminently worth it to many researchers, because it lets them study the brain on its own terms.

    2
    Courtesy of The Allen Institute.

    To Hubel and Wiesel, the brain looked like an assembly line: groups of neurons, each specialized for a specific role, dividing and conquering each task. Show someone a red balloon, and neurons sensitive to red and circles will respond independently. But that approach never really suited how the brain actually functions—it is so densely wired up that no neuron is ever acting in isolation. “The brain is not looking at one neuron at a time,” says Stefano Fusi, professor of neuroscience at Columbia University. “Neurons, they’re looking at thousands of other neurons. So we should take the same perspective.”

    Regions like the prefrontal cortex, where every neuron responds to a whole host of things, seem to operate much more like a workshop, in which each artisan has expertise in a wide range of tasks. Some might have particular talents for throwing raw clay, and others might be especially skilled at applying glaze—and when they work together, they can craft a variety of objects. This diversity is an advantage, and it’s likely essential to the complex problem-solving and reasoning skills at which humans so excel. (In a study of the prefrontal cortex [Nature (below)], Fusi demonstrated that, when neuronal populations show a rich diversity of responses to different situations, monkeys tend to perform better on a memory task.) Neuron populations that are highly specialized, on the other hand, are inflexible, much like an assembly line: They can only accomplish so many different things.

    Assembly lines, though, are extremely easy to understand. Each step in the process can be examined independently to figure out precisely how it contributes to the overall product. But the artisans in a highly interactive workshop can’t be viewed in isolation, and neither can neurons in regions like the prefrontal cortex. And these collective activity patterns are too complicated for humans to grasp without the aid of mathematical tools. “It’s not something that you can visualize,” Fusi says.

    So neuroscientists use an approach called “dimensionality reduction” to make such visualization possible—they take data from thousands of neurons and, by applying clever techniques from linear algebra, describe their activities using just a few variables. This is just what psychologists did in the 1990s to define their five major domains of human personality: openness, agreeableness, conscientiousness, extroversion, and neuroticism. Just by knowing how an individual scored on those five traits, they found, they could effectively predict how that person would answer hundreds of questions on a personality test.

    But the variables extracted from neural data can’t be expressed in a single word like “openness.” They are more like motifs, patterns of activity that span whole neural populations. A few of these motifs can define the axes of a plot, wherein every point represents a different combination of those motifs—its own unique activity profile.

    There are downsides to reducing data from thousands of neurons down to just a few variables. Just like taking a 2D image of a 3D cityscape renders some buildings totally invisible, cramming a complex set of neuronal data down into only a few dimensions eliminates a great deal of detail. But working in a few dimensions is much more manageable than examining thousands of individual neurons at once. Scientists can plot evolving activity patterns on the axes defined by the motifs to watch how the neurons’ behavior changes over time. This approach has proven especially fruitful in the motor cortex, a region where confusing, unpredictable single-neuron responses had long flummoxed researchers. Viewed collectively, however, the neurons trace regular, often circular trajectories. Features of these trajectories correlate with particular aspects of movement—their location, for example, is related to speed [eLife (below)].

    Olsen says he expects that scientists will use dimensionality reduction to extract interpretable patterns from the complex data. “We can’t go neuron by neuron,” he says. “We need statistical tools, machine learning tools, that can help us find structure in big data.”

    But this vein of research is still in its early days, and scientists struggle to agree on what the patterns and trajectories mean. “People fight all the time about whether these things are factual,” says John Krakauer, professor of neurology and neuroscience at Johns Hopkins University. “Are they real? Can they be interpreted as easily [as single-neuron responses]? They don’t feel as grounded and concrete.”

    Bringing these trajectories down to earth will require developing new analytical tools, says Churchland—a task that will surely be facilitated by the availability of large-scale data sets like the Allen Institute’s. And the unique capacities of the institute, with its deep pockets and huge research staff, will enable it to produce greater masses of data to test those tools. The institute, Olsen says, functions like an astronomical observatory—no single lab could pay for its technologies, but the entire scientific community benefits from, and contributes to, its experimental capabilities.

    Currently, he says, the Allen Institute is working on piloting a system where scientists from across the research community can suggest what sorts of stimuli animals should be shown, and what sorts of tasks they should be doing, while thousands of their neurons are being recorded. As recording capacities continue to increase, researchers are working to devise richer and more realistic experimental paradigms, to observe how neurons respond to the sorts of real-world, challenging tasks that push their collective capabilities. “If we really want to understand the brain, we cannot keep just showing oriented bars to the cortex,” Fusi says. “We really need to move on.”

    Science papers:
    Nature
    Allen Brain Map
    Nature
    eLife

    See the full article here .

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  • richardmitnick 9:11 am on September 28, 2022 Permalink | Reply
    Tags: "A Wheel Made of ‘Odd Matter’ Spontaneously Rolls Uphill", , , Physicists have solved a key problem of robotic locomotion by revising the usual rules of interaction between simple component parts., , , WIRED   

    From “Quanta Magazine” Via “WIRED“: “A Wheel Made of ‘Odd Matter’ Spontaneously Rolls Uphill” 

    From “Quanta Magazine”

    Via

    “WIRED“

    9.25.22
    Ben Brubaker

    Physicists have solved a key problem of robotic locomotion by revising the usual rules of interaction between simple component parts.

    1
    In cycling through a sequence of shapes, an odd wheel propels itself up steep and bumpy terrain.Illustration: Samuel Velasco/Quanta Magazine

    In a physics lab in Amsterdam, there’s a wheel that can spontaneously roll uphill by wiggling.

    This “odd wheel” looks simple: just six small motors linked together by plastic arms and rubber bands to form a ring about 6 inches in diameter. When the motors are powered on, it starts writhing, executing complicated squashing and stretching motions and occasionally flinging itself into the air, all the while slowly making its way up a bumpy foam ramp.

    “I find it very playful,” said Ricard Alert, a biophysicist at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, who was not involved in making the wheel. “I liked it a lot.”

    The odd wheel’s unorthodox mode of travel exemplifies a recent trend: Physicists are finding ways to get useful collective behavior to spontaneously emerge in robots assembled from simple parts that obey simple rules. “I’ve been calling it robophysics,” said Daniel Goldman, a physicist at the Georgia Institute of Technology.

    The problem of locomotion—one of the most elementary behaviors of living things—has long preoccupied biologists and engineers alike. When animals encounter obstacles and rugged terrain, we instinctively take these challenges in stride, but how we do this is not so simple. Engineers have struggled to build robots that won’t collapse or lurch forward when navigating real-world environments, and they can’t possibly program a robot to anticipate all the challenges it might encounter.

    The odd wheel, developed by the physicists Corentin Coulais of the University of Amsterdam and Vincenzo Vitelli of the University of Chicago and collaborators and described in a recent preprint, embodies a very different approach to locomotion. The wheel’s uphill movement emerges from simple oscillatory motion in each of its component parts. Although these parts know nothing about the environment, the wheel as a whole automatically adjusts its wiggling motion to compensate for uneven terrain.


    Energy generated during each cyclical oscillation of the odd wheel allows it to push off against the ground and roll upward and over obstacles. (Another version of the wheel with only six motors was studied in a recent paper.)Video: Corentin Coulais.

    The physicists also created an “odd ball” that always bounces to one side and an “odd wall” that controls where it absorbs energy from an impact. The objects all stem from the same equation describing an asymmetric relationship between stretching and squashing motions that the researchers identified two years ago.

    “These are indeed behaviors you would not expect,” said Auke Ijspeert, a bioroboticist at the Swiss Federal Institute of Technology Lausanne. Coulais and Vitelli declined to comment while their latest paper is under peer review.

    In addition to guiding the design of more robust robots, the new research may prompt insights into the physics of living systems and inspire the development of novel materials.

    Odd Matter

    The odd wheel grew out of Coulais and Vitelli’s past work on the physics of “active matter”—an umbrella term for systems whose constituent parts consume energy from the environment, such as swarms of bacteria, flocks of birds and certain artificial materials. The energy supply engenders rich behavior, but it also leads to instabilities that make active matter difficult to control.

    Physicists have historically focused on systems that conserve energy, which must obey principles of reciprocity: If there’s a way for such a system to gain energy by moving from A to B, any process that takes the system from B back to A must cost an equal amount of energy. But with a constant influx of energy from within, this constraint no longer applies.

    In a 2020 paper in Nature Physics [below], Vitelli and several collaborators began to investigate active solids with nonreciprocal mechanical properties. They developed a theoretical framework in which nonreciprocity manifested in the relationships between different kinds of stretching and squashing motions. “That to me was just a beautiful mathematical framework,” said Nikta Fakhri, a biophysicist at the Massachusetts Institute of Technology.

    Suppose you squash one side of a solid, causing it to bulge outward in a perpendicular direction. You can also stretch and squash it along an axis rotated by 45 degrees, distorting it into a diamond shape. In an ordinary, passive solid, these two modes are independent; deforming the solid in one direction does not deform it along either diagonal.

    In an active solid, the researchers showed that the two modes can instead have a nonreciprocal coupling: Squashing the solid in one direction will also squash it along the axis rotated by 45 degrees, but squashing along this diagonal will stretch it, not squash it, along the original axis. Mathematically, the number describing the coupling between these two modes is positive going one way and negative going the other way. Because of the sign difference, the physicists call the phenomenon “odd elasticity.”

    In an odd elastic solid, undoing a deformation isn’t as simple as reversing the stretching and squashing motions that produced it; instead, the cycle of deformations that returns the solid to its starting configuration can leave it with some excess energy. This has striking consequences, such as enabling uphill locomotion of the odd wheel.

    Meanwhile Coulais, an experimentalist, was studying [Nature Communications (below] nonreciprocity in robotic active matter consisting of a chain of simple modules, each outfitted with a motor, sensor and microcontroller. With these sensing and control capabilities, Coulais could use feedback loops to program each module to respond nonreciprocally to the movements of its neighbors.

    Fig. 1
    2
    Asymmetric and unidirectionally amplified waves in a nonreciprocal mass-and-spring model. a Schematic representation of the nonreciprocal mass-and-spring model. b Magnitude of the solutions of Eq. (1) in the frequency domain exp(i(ωt−q±x)) vs. spatial coordinate, for three different frequencies. c Green’s function of Eq. (1) vs. time and spatial coordinate. In (b) and (c), ε = 0.9 and c = 0.5

    Fig. 2
    3
    Robotic metamaterial with nonreciprocal interactions. a Robotic metamaterial made of 10 unit cells mechanically connected by soft elastic beams (i). Scale bar: 2 cm. (bc) Closeup b and sketch c on two unit cells. Each unit cell is a minimal robot with a unique rotational degree of freedom that comprises an angular sensor (ii), a coreless DC motor (iii), and a microcontroller (iv). Each unit cell communicates with its right neighbor via electric wires (v). These components allow to program a control loop characterized by the feedback parameter α (see main text for definition). d Rescaled torsional stiffnesses CL→R/C (red) and CR→L/C (blue) as a function of the feedback parameter

    More instructive images are available in the science paper.

    The two physicists, former colleagues at Leiden University in the Netherlands, then teamed up to develop robotic active matter that would embody the mathematics of odd elasticity.

    Uncommon Oscillations

    Ordinary elasticity—the springiness of matter—is a bulk property that emerges from springlike interactions between matter’s microscopic constituents. Coulais and Vitelli sought to put an odd twist on the elastic interactions between robotic modules.

    In their new design, each module consisted of a motor controlling the rotation of two plastic arms, with rubber bands supplying springiness by pulling back on the arms. The researchers started with a pair of modules sharing an arm. Sensors and controllers on the modules implemented a nonreciprocal feedback loop: A clockwise turn of the first one’s motor would generate a clockwise torque on the second one’s motor, but a clockwise rotation of the second motor would induce a counterclockwise torque on the first.

    This arrangement is inherently unstable. Left undisturbed, the modules will sit still forever, but even the slightest nudge will give rise to an unending tug of war: Whichever way a motor turns, its interaction with the other motor pushes it back in the opposite direction. If the coupling between the modules is strong enough, the arms will start oscillating back and forth with increasing amplitude.

    On a 2D plot with axes representing the two motor angles, these growing oscillations will appear as an outward spiral, gaining energy on each cycle like a runner descending an Escher staircase and picking up speed with each lap. But the motors can only put out so much torque, and energy is lost to friction, so the amplitude of the oscillations eventually tops out. On the 2D plot of motor angles, the spiraling trajectory converges to a circle, then keeps retracing its path exactly. Physicists call this self-sustained, constant-amplitude oscillation a limit cycle.

    The modules’ limit-cycle oscillations represent a victory of stable, regular motion over the chaos that so often plagues complex systems. Consider the chaotic “double pendulum,” which consists of one pendulum hanging from another: Small changes in its initial conditions soon lead to totally different trajectories through space. Limit cycles are the opposite phenomenon: Different initial conditions ultimately yield the same trajectory. In the case of Coulais and Vitelli’s odd modules, regardless of which arm was initially nudged and in which direction, the system eventually exhibits the same steady-state oscillations.

    This key feature makes limit-cycle oscillations more special than, say, the familiar cyclical motion of a (single) pendulum. On a 2D plot of a pendulum’s position and velocity, its oscillations appear as orbits around a closed loop, but if you start the pendulum swinging at different speeds, it’ll trace a larger or smaller circle. Limit-cycle oscillations are much more robust: Many trajectories that start out different converge on exactly the same orbit, and if the system is nudged away from this orbit, it’ll get pulled back in.

    These limit-cycle oscillations offered the researchers a way to tame the unruly dynamics of active matter and put it to work.

    Behind the Wheel

    Now that Coulais and Vitelli had engineered the building blocks of odd matter, it was time to assemble them. Many modules connected in the right way would resemble the odd elastic solid Vitelli had initially envisioned. What would happen if these modules were linked together with shared arms to form a wheel?

    When the team supplied power to the motors, the loop began to oscillate, interweaving stretching and squashing with similar motions angled at 45 degrees. It switched back and forth between the two modes of self-deformation in Vitelli’s theory of odd elasticity. The limit-cycle oscillations of adjacent motors generated a limit cycle in the collective motion of the wheel as a whole. The oddness of the motors’ coupling singled out a direction for the wheel’s locomotion, much as an Escher staircase breaks the symmetry between clockwise and counterclockwise laps—it’s all downhill one way and all uphill the other way. The energy generated during each limit cycle allowed the wheel to push off against the ground and roll upward.

    4
    Odd interactions between adjacent robotic modules can also be utilized to construct an odd wall.Courtesy of Corentin Coulais.

    It’s hard to pin down why the wheel’s uphill locomotion is so robust, precisely because its limit cycle is an emergent phenomenon, not seen when you scrutinize any individual module. Nick Gravish, a roboticist at the University of California-San Diego, suspects that the limit-cycle oscillations of each pair of motors greatly restrict the possible collective motions of the wheel. He noted that the emergence of collective motion from low-level oscillations has parallels in biology: “Animals are lots of interconnected oscillatory components that have to work together.”

    Coulais and Vitelli also explored the effects of odd couplings on collisions. They showed that an odd ball—a projectile assembled from odd modules—would always bounce off in a specific direction when launched without any spin, while an odd wall could control the direction in which it absorbed energy from a projectile. These functions could prove useful in the design of new active materials, said Denis Bartolo, a physicist at the École Normale Supérieure in Lyon, France, adding that “the next huge step to be made would be to find a way to self-assemble these machines.”

    Robophysics

    Before the recent experiments, it wasn’t obvious that odd interactions would give rise to locomotion. Each motor responds only to its neighbors, and yet the wheel moves forward. This absence of top-down control is especially intriguing to biologists seeking to understand how swarms cooperate without designated leaders, and how primitive animals without nervous systems seek out food.

    The emergent locomotion of the odd wheel is appealing to researchers largely because the wheel’s building blocks are so simple. “You can just be lost in the complexity of living systems,” said Alert. He pointed to a famous quote from Richard Feynman: “What I cannot create, I do not understand.”

    Coulais and Vitelli developed their odd modules without mimicking any specific living system, so it’s an open question whether biology has made use of the same emergent dynamics. M. Cristina Marchetti, a theoretical physicist at the University of California-Santa Barbara, called the result “very interesting,” and said the next step to understanding its possible role in biology is to see how well the behavior persists in a noisy environment like that of a living cell.

    But whereas evolution often finds good solutions to problems, it can miss opportunities. The odd wheel might be a true novelty. Bartolo notes that, in the design of robots, machines and materials, bioinspiration has its limits: “If you tried to make a plane using beating wings, you would still be walking or swimming from Normandy to New York.”

    Science papers:
    Nature Physics
    Nature Communications

    See the full article here .

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  • richardmitnick 8:21 am on September 28, 2022 Permalink | Reply
    Tags: "The Secret Microscope That Sparked a Scientific Revolution", A lens 10 times more powerful than anything built before it- a design which wouldn’t be bested for another 150 years., , “Letter 18”: Van Leeuwenhoek (lay-u-when-hoke) had looked everywhere and found what he called animalcules (Latin for “little animals”) in everything., , Despite the prodigious genius of Galileo and Hooke neither produced lenses with anything close to the magnifying power of Van Leeuwenhoek’s., Germ theory, How a Dutch fabric seller became the first person ever to see a microorganism., How did he do it? How did a shopkeeper build a microscopic lens that surpassed the world’s greatest by an order of magnitude?, , , Microorganisms are the second most abundant life-forms on Earth., Neutron tomography, Only one lens survives today that produces the 270X magnification Van Leeuwenhoek used to make his greatest discovery., Two of the types that Van Leeuwenhoek identified-protozoa and bacteria-responsible for more than half the deaths of every human who has ever lived., Van Leeuwenhoek became the first person to ever see a microorganism., Van Leeuwenhoek crafted more than 500 microscopes but only 11 of his instruments survive today., Van Leeuwenhoek had no idea about the pivotal role his little animals played., Van Leeuwenhoek zealously guarded how he made his revolutionary lens., WIRED   

    From “WIRED“: “The Secret Microscope That Sparked a Scientific Revolution” 

    From “WIRED“

    9.27.22
    Cody Cassidy

    1
    Illustration: Ariel Davis.

    How a Dutch fabric seller made the most powerful magnifying lens of his time—and of the next 150 years—and became the first person ever to see a microorganism.

    “On September 7, 1674, Antonie Van Leeuwenhoek, a fabric seller living just south of The Hague, Netherlands, burst forth from scientific obscurity with a letter to London’s Royal Society detailing an astonishing discovery. While he was examining algae from a nearby lake through his homemade microscope, a creature “with green and very glittering little scales,” which he estimated to be a thousand times smaller than a mite, had darted across his vision.

    Two years later, on October 9, 1676, he followed up with another report so extraordinary that microbiologists today refer to it simply as “Letter 18”: Van Leeuwenhoek (lay-u-when-hoke) had looked everywhere and found what he called animalcules (Latin for “little animals”) in everything.

    He found them in the bellies of other animals, his food, his own mouth, and other people’s mouths. When he noticed a set of remarkably rancid teeth, he asked the owner for a sample of his plaque, put it beneath his lens, and witnessed “an inconceivably great number of little animalcules” moving “so nimbly among one another, that the whole stuff seemed alive.” After a particularly uncomfortable evening, which he blamed on a fatty meal of hot smoked beef, he examined his own stool beneath his lens and saw animalcules that were “somewhat longer than broad, and their belly, which was flat-like, furnished with sundry little paws”—a clear description of what we now know as the parasite giardia.

    With his observations of these fast, fat, and sundry-pawed creatures, Van Leeuwenhoek became the first person to ever see a microorganism—a discovery of almost incalculable significance to human health and our understanding of life on this planet.

    Microorganisms are the second most abundant life-forms on Earth. Two of the types that Van Leeuwenhoek identified—protozoa and bacteria—are by some estimates responsible for more than half the deaths of every human who has ever lived, and yet until he observed them their existence had hardly been seriously postulated, much less proven. Of course, he had no idea about the pivotal role his little animals played, but his revelation provided the foundation for germ theory—the greatest leap forward in the history of medicine. Even more surprising, this monumental discovery was not made by one of the 17th century’s great scientific minds such as Galileo or Isaac Newton. Instead, a secretive, obsessive, self-taught Dutchman of little renown did it by handcrafting a lens 10 times more powerful than anything built before it. His design wouldn’t be bested for another 150 years.

    Yet even as scientists steadily unlocked the secrets of Van Leeuwenhoek’s microworld over the past 350 years, one great mystery eluded them: How the hell did he do it? How did a shopkeeper working during his off hours build a microscopic lens that surpassed the world’s greatest by an order of magnitude?

    While Leeuwenhoek shared nearly everything he saw through his microscope in exactingly detailed letters, he zealously guarded how he made his revolutionary lens. When asked, he declined or obfuscated. Even as his discoveries made him so famous that the King of England requested to see his animalcules and Peter the Great stopped in Delft to see his lenses, the Dutchman never revealed his secrets.

    Van Leeuwenhoek crafted more than 500 microscopes but only 11 of his instruments survive today—and only one that produces the 270X magnification he used to make his greatest discovery. Because that lens remains sandwiched between brass plates, determining its mode of manufacture would require disassembling the microscope—an affront tantamount to scraping paint off the Mona Lisa to determine the sequence of Leonardo’s brush strokes.

    Most of Van Leeuwenhoek’s contemporaries believed he had invented a new glassblowing technique. Clifford Dobell, who wrote the brilliant 1960 biography Antony Van Leeuwenhoek and His Little Animals, postulated that he created his best lenses by simply grinding and polishing them better than anyone else. But in three centuries of speculation, no one could say for sure.

    Tiemen Cocquyt’s interest in Van Leeuwenhoek’s secrets began in the late 2000s, soon after first seeing one of his microscopes, which was then locked away in the basement of the University Museum Utrecht. “How could this toy open up the microworld?” Cocquyt remembers thinking.

    Cocquyt is a curator in the National Museum Boerhaave in Leiden, Netherlands, which houses an array of early optical instruments, including several of the microscopes. He has spent much of his career investigating the origins of Europe’s 17th-century optical revolution, when visual instruments suddenly leaped from simple magnifiers to the great telescopes of Galileo and Christiaan Huygens. (That revolution was inadvertently sparked, Cocquyt says, by Italian advances in making ultra-clear glass.)

    Over Zoom, Cocquyt shows me a replica of a Van Leeuwenhoek microscope, and it does look like a toy—a doll’s hand mirror, to be exact. It’s barely 3 inches tall, with a thin handle leading to a square brass plate. The lens sits beneath a pinhole in the plate’s center, and on the back side a pin for holding samples is connected to a set of screws for focal adjustment.

    When Cocquyt first examined the exposed glass of the lens, he believed its smooth surface indicated it could only have been created by heat. Thus, like many of Van Leeuwenhoek’s contemporaries, he suspected the Dutchman had invented a new glassblowing technique. But without looking inside, he could only speculate.

    The definitive answer, he hoped, might be found with the help of a nuclear reactor.

    At its simplest, a magnifying lens is nothing more than a curved piece of transparent material—usually glass. As light passes through that angled glass, it decelerates, and its path is redirected, or refracted. Depending on its design, a lens can manipulate light in any number of ways, but magnifying lenses like Van Leeuwenhoek’s are spherical—technically called bi-convex—and refract light into a single focal point. “In essence, it serves as a light funnel,” says Steve Ruzin, curator of the Golub Collection of antique microscopes at The University of California-Berkeley. Place your eye at the narrow end of the funnel, and an enormous amount of light arriving from the lens’s focal point crams through your pupil.

    This has two effects. First, the more light your eye receives from an object, the more detail it can perceive. Second, by funneling all the light hitting the lens through the width of your pupil, the image consumes your entire field of view. An object that once projected onto your retina as an undetectable speck now appears in Imax.

    Of course, not all spherical lenses magnify equally. A big lens with a gentle curve refracts the light traveling through it only slightly, and thus barely enlarges the image. A small lens with a sharp curve refracts the light more, enlarging the image a great deal. Moderately powered spherical lenses of the 17th century were about the size of a pea. Van Leeuwenhoek’s greatest lenses were smaller than a sixth that size. At that diameter, construction becomes exceptionally difficult. Even the smallest manufacturing defect—a bubble, scuff, or scratch—could project an enormously disfiguring visual aberration. Larger, less powerful lenses are far more forgiving. They are simple enough to create that they’ve been found among remnants of the oldest civilizations. The earliest-known handcrafted lens is a piece of ground rock crystal capable of 3X magnification that archeologists discovered in a nearly 3,000-year-old Assyrian palace. But because glass occurs naturally, its magnifying power has probably been independently discovered and harnessed many times throughout history.

    Nevertheless, lenses never exceeded much beyond the power of typical modern reading glasses until the early 1590s, when a Dutch lens maker named Hans Janssen built a microscope capable of 9X magnification. Janssen’s contraption inspired many copycats, one of which intrigued Galileo, who modified one of his own telescopes to produce a microscope that one witness claimed could show “flies which appear large as a lamb.”

    In 1665—only a few years before Van Leeuwenhoek peered through his first lens—microscopes emerged into the public consciousness when the polymath Robert Hooke published his surprise bestseller Micrographia. The book included Hooke’s observations, interpretations, illustrations, and even simple instructions on how anyone could make their own lenses: Hold a thin hair of glass over a flame until a bead forms, ‘which will hang at the end of the thread,’ writes Hooke. Snap off the bead, and the result is a spherical magnifier.

    But despite the prodigious genius of Galileo and Hooke neither produced lenses with anything close to the magnifying power of Van Leeuwenhoek’s. “Leeuwenhoek took an opportunity that lay somehow undeveloped in the 1660s and pushed it into the best result that was possible,” Cocquyt says.

    He did so by first eschewing Hooke’s and Galileo’s preference for using multiple lenses arranged in sequence. This design is common in modern microscopes—it’s a bit like projecting an image into another projector—but achieving that magnifying effect without producing huge distortions requires extreme precision. Until that challenge was solved in the early 19th century, single-lens microscopes like Van Leeuwenhoek’s could achieve far superior results.

    Hooke was aware of this shortcoming in his design, yet he still preferred multiple lenses, thanks in part to their ease of use. High-powered lenses have such an extremely short focal point that with just one, the viewer has to place their eye incredibly close to the lens, making blinking difficult. Hooke wrote that he found single-lens microscopes “offensive to my eye.” Ruzin told me that looking through one of Van Leeuwenhoek’s surviving devices is “terribly uncomfortable.”

    Van Leeuwenhoek’s design may have been torture to use, but it was also brilliant—and that brilliance extended beyond his super-powered lenses. Because his device was handheld, he could backlight his sample by holding it up against sunlight or a flame, while his contemporaries’ desk-bound microscopes could only be lit from above. Top-down lighting works well for opaque objects, such as a bee’s stinger, but not for pond water and other translucent samples, where it’s far easier to see microorganisms. To observe these liquids, Van Leeuwenhoek filled a small glass capsule, glued it to the microscope’s pin, and held the instrument up to light.

    “It almost seems as if Van Leeuwenhoek knew that a new microworld was to unfold,” Cocquyt told me. One of his scientific rivals, Johannes Hudde, later said, “isn’t it surprising that we never had the creativity to use these ball lenses to observe little things against the daylight, and that an uneducated and ignorant man such as Van Leeuwenhoek had to be the one to teach this to us.”

    Van Leeuwenhoek was the fifth son of a basket maker, born in the Delft—a small port city in South Holland known for its picturesque waterways, pottery, and beer. At 16 he departed for an apprenticeship as a dry goods seller in Amsterdam, but six years later he returned home, married the daughter of a well-regarded local brewer, and purchased his own fabric shop.

    He spent his twenties growing a successful business but suffered immense personal tragedy. Of the five children he and his wife Barbara had in their 12 years of marriage, four died in infancy; Barbara would soon follow. Few biographical details have survived from his first decade back in Delft, but he held a number of odd jobs in addition to running his draper shop, including working as chief custodian of the local courthouse. A stint as town surveyor offers one clue to Van Leeuwenhoek’s budding scientific potential: proof he had learned geometry.

    His obsession with magnifying lenses began sometime in his mid-thirties. How he came upon it isn’t known. His writings never touch on its origins. Perhaps, as many have speculated, he started using lenses to inspect the quality of his cloth. Or maybe he got caught up in the public mania for microscopes following the publication of Hooke’s Micrographia. Van Leeuwenhoek never mentions the book in any of his letters, but the timing aligns, and he clearly read it: Some of his experiments replicate Hooke’s too closely to be a coincidence. But regardless of how Van Leeuwenhoek got into microscopy, by 1668 he had begun pursuing it with an unusual tenacity. While traveling in England that year, he saw the white cliffs of Dover and felt compelled to examine their chalky slopes beneath his lens: “I observed that chalk consisteth of very small transparent particles; and these transparent particles lying one upon another, is, methinks now, the reason why chalk is white.”

    By 1673, though still operating in complete obscurity, he was already making the world’s most powerful lenses. His obscurity might very well have continued, and the momentous discovery of microorganisms might well have served only to satisfy this curious individual’s psychological compulsion, were it not for a Delft physician named Renier de Graaf.

    De Graaf had come to some renown through his experiments using dyes to determine organ function, and in 1673 he introduced Van Leeuwenhoek to the Royal Society with a note calling him a “most ingenious person … who has devised microscopes which far surpass those which we have hitherto seen.” Following that preamble, Van Leeuwenhoek described the body parts of a louse in his precise-yet-meandering writing style that is, as one biographer notes, “distinguished with a certain business formality, but an almost total lack of coherence.” Over the next year, he sent five more letters to the Royal Society conveying interesting but not particularly controversial observations about the globules in milk and the structure of his fingernails. Then, on September 7, 1674, he sent the letter reporting his shocking discovery: Within an otherwise unremarkable drop of pond water he had seen “glittering” creatures a thousand times smaller than any animal he had previously observed.

    The Society’s secretary, Henry Oldenburg, replied to Van Leeuwenhoek with understandable restraint: “This phenomenon, and some of the following ones seeming to be very extraordinary, the author hath been desired to acquaint us with his method of observing, that others may confirm such observations as these.” Van Leeuwenhoek quickly responded, providing eyewitness accounts of a few local dignitaries who had looked through his lenses—but refused to disclose the secrets of his techniques. “My method for seeing the very smallest animalcules and minute eels, I do not impart to others; nor how to see very many animalcules at one time. That I keep for myself alone,” he wrote. Even when Hooke himself, who learned to speak Dutch just so he could communicate with Van Leeuwenhoek without translation, specifically asked how he made his observations, the stubborn scientist refused for reasons that were, as Hooke later wrote, “best known to himself.”

    Three years later, after a few failed attempts by others, Hooke finally managed to re-create Van Leeuwenhoek’s experiment well enough to prove his observations at a gathering of the Royal Society. The confirmation made the Dutch draper famous, but despite repeated inquiry he took his secrets to the grave.

    In 2018, Cocquyt and his team of researchers set out to reveal them without taking Van Leeuwenhoek’s 350-year-old microscope apart. That’s where the nuclear reactor comes in.

    Neutron tomography is a scanning technique that is as remarkable as it is completely insane. It involves blasting neutrons generated by atomic collisions through a large-caliber barrel—which sticks out of a reactor’s nuclear chamber like the devil’s cannon—and into whatever object needs scanning. Neutrons, beyond irradiating everything they hit, pass right through metals but slam into most low-mass elements, including those in glass. Sensors behind the object detect the neutrons, producing an image that reveals their inner structure. Recent scans have led to the discovery of a dinosaur inside another dinosaur’s belly and the remnants of ice in martian meteorites.

    A nuclear reactor in Van Leeuwenhoek’s hometown of Delft had recently installed a neutron tomography instrument, and Cocquyt used it to examine the Dutchman’s lenses in their birthplace. He first placed a replica microscope in front of the neutron scanner—a test to ensure he didn’t render a priceless piece of scientific history radioactive for 1,000 years. When he next scanned the inventor’s less-powerful microscopes, the images clearly showed the glass to have hard edges and a slight lentil shape. “Exactly what you would expect for a ground lens,” Cocquyt says.

    But on his most powerful lens, neutron tomography revealed that Van Leeuwenhoek used another technique entirely. It was almost perfectly spherical and completely smooth, without the sharp rim inevitably created by a traditional grinding cup. Even more tellingly, the lens retained the faint remnants of a snapped stem, concealed by the brass plates since the day Van Leeuwenhoek had placed it there.

    The stem is a smoking gun. It’s the unavoidable result of forming a lens by melting a thread of glass until a bead forms on its end and then snapping it off. In other words, to make his greatest lens, Van Leeuwenhoek copied Hooke’s simple recipe from the book that likely inspired him. Cocquyt believes this may explain why he was so circumspect when Hooke asked about his methods; he wanted to avoid giving credit to Hooke himself.

    Published in Science Advances [below] last year, Cocquyt’s discovery that Van Leeuwenhoek used a well-known technique reveals a deeper truth about the state of microscopy in the 17th century. It suggests that for all the crafting genius required to make his tiny, super-powered lens, Van Leeuwenhoek’s greatest insight may have been that there was something new to see by making one.

    Fig. 1 The two original Van Leeuwenhoek microscopes that were studied with neutron tomography.
    2
    The lens sits mounted between the brass plates, at the position of the specimen pin. (A) A medium-powered (×118) instrument (Rijksmuseum Boerhaave, Leiden, inventory number V7017). Note that there is a redundant drill hole in the upper left corner of the instrument, not to be confused with its lens aperture, which is directly behind the pin. This microscope is numbered #1 by Van Zuylen. Photo credit: Tom Haartsen Fotografie, Ouderkerk aan de Amstel. (B) The instrument with the highest magnification among the preserved ones (×266) (Utrecht University Museum, inventory number UM-1). This microscope is numbered #3 by Van Zuylen. Photo credit: Utrecht University Museum.

    Fig. 4 Orthogonal cross sections of computed tomography of the Van Leeuwenhoek microscopes from Leiden and Utrecht.
    3
    (A) The cross sections of the lentil-shaped lens of the medium-powered microscope (V7017). (B) The circular cross section of the high-powered microscope (UM-1). The XZ projection shows that this ball-shaped lens has a tiny glass stem connected to it.

    [More instructive images are available in the science paper.]

    This seems intuitive and incredibly obvious to a modern reader. What kind of scientist wouldn’t want to see in greater detail? But before Van Leeuwenhoek, most microscopists used their lenses to reveal greater detail about the visible world—things they could already see to some degree with the naked eye. Their drawings of bee stingers and ant legs do not lose their resemblance to the creatures readers were familiar with. Had they used Van Leeuwenhoek’s high-powered lenses, their depictions would not have been recognizable to anyone.

    Leeuwenhoek had no inkling that minuscule, alien-like creatures awaited him, but his obsession with the microworld drove him to leave the visible world behind and discover a vast new microbial one living under—and inside—our noses.”

    Science paper:
    Science Advances

    See the full article here .

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    Please help promote STEM in your local schools.

    Stem Education Coalition

     
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