Pie charts and scatter plots seem like ordinary tools, but they revolutionized the way we solve problems. From a report: John Carter has only an hour to decide. The most important auto race of the season is looming; it will be broadcast live on national television and could bring major prize money. If his team wins, it will get a sponsorship deal and a chance to start making some real profits for a change. There's just one problem. In seven of the past twenty-four races, the engine in the Carter Racing car has blown out. An engine failure live on TV will jeopardize sponsorships -- and the driver's life. But withdrawing has consequences, too. The wasted entry fee means finishing the season in debt, and the team won't be happy about the missed opportunity for glory. As Burns's First Law of Racing says, "Nobody ever won a race sitting in the pits." One of the engine mechanics has a hunch about what's causing the blowouts. He thinks that the engine's head gasket might be breaking in cooler weather. To help Carter decide what to do, a graph is devised that shows the conditions during each of the blowouts: the outdoor temperature at the time of the race plotted against the number of breaks in the head gasket. The dots are scattered into a sort of crooked smile across a range of temperatures from about fifty-five degrees to seventy-five degrees. The upcoming race is forecast to be especially cold, just forty degrees, well below anything the cars have experienced before. So: race or withdraw? This case study, based on real data, and devised by a pair of clever business professors, has been shown to students around the world for more than three decades. Most groups presented with the Carter Racing story look at the scattered dots on the graph and decide that the relationship between temperature and engine failure is inconclusive. Almost everyone chooses to race. Almost no one looks at that chart and asks to see the seventeen missing data points -- the data from those races which did not end in engine failure.

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A series of problem-solving experiments reveal that people are more likely to consider solutions that add features than solutions that remove them, even when removing features is more efficient. Nature reports: Across a series of [...] experiments, the authors observe that people consistently consider changes that add components over those that subtract them -- a tendency that has broad implications for everyday decision-making. For example, Adams et al. and colleagues analyzed archival data and observed that, when an incoming university president requested suggestions for changes that would allow the university to better serve its students and community, only 11% of the responses involved removing an existing regulation, practice or program. Similarly, when the authors asked study participants to make a 10 x 10 grid of green and white boxes symmetrical, participants often added green boxes to the emptier half of the grid rather than removing them from the fuller half, even when doing the latter would have been more efficient. Adams et al. demonstrated that the reason their participants offered so few subtractive solutions is not because they didn't recognize the value of those solutions, but because they failed to consider them. Indeed, when instructions explicitly mentioned the possibility of subtractive solutions, or when participants had more opportunity to think or practice, the likelihood of offering subtractive solutions increased. It thus seems that people are prone to apply a 'what can we add here?' heuristic (a default strategy to simplify and speed up decision-making). This heuristic can be overcome by exerting extra cognitive effort to consider other, less-intuitive solutions.

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ZDNet reports: Scientists from quantum computing company D-Wave have demonstrated that, using a method called quantum annealing, they could simulate some materials up to three million times faster than it would take with corresponding classical methods. Together with researchers from Google, the scientists set out to measure the speed of simulation in one of D-Wave's quantum annealing processors, and found that performance increased with both simulation size and problem difficulty, to reach a million-fold speedup over what could be achieved with a classical CPU... The calculation that D-Wave and Google's teams tackled is a real-world problem; in fact, it has already been resolved by the 2016 winners of the Nobel Prize in Physics, Vadim Berezinskii, J. Michael Kosterlitz and David Thouless, who studied the behavior of so-called "exotic magnetism", which occurs in quantum magnetic systems.... Instead of proving quantum supremacy, which happens when a quantum computer runs a calculation that is impossible to resolve with classical means, D-Wave's latest research demonstrates that the company's quantum annealing processors can lead to a computational performance advantage... "What we see is a huge benefit in absolute terms," said Andrew King, director of performance research at D-Wave. "This simulation is a real problem that scientists have already attacked using the algorithms we compared against, marking a significant milestone and an important foundation for future development. This wouldn't have been possible today without D-Wave's lower noise processor." Equally as significant as the performance milestone, said D-Wave's team, is the fact that the quantum annealing processors were used to run a practical application, instead of a proof-of-concept or an engineered, synthetic problem with little real-world relevance. Until now, quantum methods have mostly been leveraged to prove that the technology has the potential to solve practical problems, and is yet to make tangible marks in the real world. Looking ahead to the future, long-time Slashdot reader schwit1 asks, "Is this is bad news for encryption that depends on brute-force calculations being prohibitively difficult?"

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An anonymous reader quotes a report from Motherboard: [A] group of researchers from the Technion in Israel and Google in Tel Aviv presented an automated conjecturing system that they call the Ramanujan Machine, named after the mathematician Srinivasa Ramanujan, who developed thousands of innovative formulas in number theory with almost no formal training. The software system has already conjectured several original and important formulas for universal constants that show up in mathematics. The work was published last week in Nature. One of the formulas created by the Machine can be used to compute the value of a universal constant called Catalan's number more efficiently than any previous human-discovered formulas. But the Ramanujan Machine is imagined not to take over mathematics, so much as provide a sort of feeding line for existing mathematicians. As the researchers explain in the paper, the entire discipline of mathematics can be broken down into two processes, crudely speaking: conjecturing things and proving things. Given more conjectures, there is more grist for the mill of the mathematical mind, more for mathematicians to prove and explain. That's not to say their system is unambitious. As the researchers put it, the Ramanujan Machine is "trying to replace the mathematical intuition of great mathematicians and providing leads to further mathematical research." In particular, the researchers' system produces conjectures for the value of universal constants (like pi), written in terms of elegant formulas called continued fractions. Continued fractions are essentially fractions, but more dizzying. The denominator in a continued fraction includes a sum of two terms, the second of which is itself a fraction, whose denominator itself contains a fraction, and so on, out to infinity. The Ramanujan Machine is built off of two primary algorithms. These find continued fraction expressions that, with a high degree of confidence, seem to equal universal constants. That confidence is important, as otherwise, the conjectures would be easily discarded and provide little value. Each conjecture takes the form of an equation. The idea is that the quantity on the left side of the equals sign, a formula involving a universal constant, should be equal to the quantity on the right, a continued fraction. To get to these conjectures, the algorithm picks arbitrary universal constants for the left side and arbitrary continued fractions for the right, and then computes each side separately to a certain precision. If the two sides appear to align, the quantities are calculated to higher precision to make sure their alignment is not a coincidence of imprecision. Critically, formulas already exist to compute the value of universal constants like pi to an arbitrary precision, so that the only obstacle to verifying the sides match is computing time.

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Just 11 months before his death in 2001, famous author Douglas Adams answered questions from Slashdot readers. And Slashdot reader Informativity still remembers how Adams (also a Doctor Who script editor) had included a supercomputer named Deep Thought in his first book which spent 7.5 million years to determine that the answer to the Ultimate Question of Life, the Universe, and Everything, was...the number 42: Turns out the entire universe is a product of the number 42, specifically 42 times the collection of lm/2t, such that l, m and t are the Planck Units. In a newly published paper, Measurement Quantization Describes the Physical Constants , both the constants and laws of nature are resolved from a simple geometry between two frames of reference, the non-discrete Target Frame of the universe and the discrete Measurement Frame of the observer. Its only and primary connection to our physical reality is a scalar, 42. Forty-two is what defines our universe from say any other version of our universe. So, while Douglas Adams may have just been picking numbers out of the sky when writing Hitchhiker's Guide to the Galaxy, it turns out he picked the right number, the one that defines ... well ... everything. In addition to presenting new descriptions for most of the physical constants (descriptions that don't reference other physical constants), the paper is also noted for presenting a classical unification of gravity and electromagnetism. One more interesting piece of trivia. Wikipedia reminds us that in January 2004, asteroid 2001 DA42 was given the permanent name 25924 Douglasadams... Brian G. Marsden, the director of the Minor Planet Center and the secretary for the naming committee, remarked that, with even his initials in the provisional designation, "This was sort of made for him, wasn't it?"

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An anonymous reader quotes a report from The Register: In 2010, Austin Sendek, then a physics student at UC Davis, created a petition seeking recognition for prefix "hella-" as an official International System of Units (SI) measurement representing 10^27. "Northern California is home to many influential research institutions, including the University of California, Davis, the University of California, Berkeley, Stanford University, and the Lawrence Livermore and Lawrence Berkeley National Laboratories," he argued. "However, science isn't all that sets Northern California apart from the rest of the world. The area is also the only region in the world currently practicing widespread usage of the English slang 'hella,' which typically means 'very,' or can refer to a large quantity (e.g. 'there are hella stars out tonight')." To this day, the SI describes prefixes for quantities for up to 10^24. Those with that many bytes have a yottabyte. If you only have 10^21 bytes, you have a zettabyte. There's also exabyte (10^18), petabyte (10^15), terabyte (10^12), gigabyte(10^9), and so on. Support for "hella-" would allow you to talk about hellabytes of data, he argues, pointing out that this would make the number of atoms in 12 kg of carbon-12 would be simplified from 600 yottaatoms to 0.6 hellaatoms. Similarly, the sun (mass of 2.2 hellatons) would release energy at 0.3 hellawatts, rather than 300 yottawatts. [...] The soonest [a proposal for a "hella-" SI could be officially adopted] is in November 2022, at the quadrennial meeting of the International Bureau of Weights and Measures (BIPM)'s General Conference on Weight and Measures, where changes to the SI usually must be agreed upon. The report notes that Google customized its search engine in 2010 to let you convert "bytes to hellabytes." A year later, Wolfram Alpha added support for "hella-" calculations. "Sendek said 'hellabyte' initially started as a joke with some college friends but became a more genuine concern as he looked into how measurements get defined and as his proposal garnered support," reports The Register. He believes it could be useful for astronomical measurements.

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Siobhan Roberts, writing for The New York Times: In March of 1970, Martin Gardner opened a letter jammed with ideas for his Mathematical Games column in Scientific American. Sent by John Horton Conway, then a mathematician at the University of Cambridge, the letter ran 12 pages, typed hunt-and-peck style. Page 9 began with the heading "The game of life." It described an elegant mathematical model of computation -- a cellular automaton, a little machine, of sorts, with groups of cells that evolve from iteration to iteration, as a clock advances from one second to the next. Dr. Conway, who died in April, having spent the latter part of his career at Princeton, sometimes called Life a "no-player, never-ending game." Mr. Gardner called it a "fantastic solitaire pastime." The game was simple: Place any configuration of cells on a grid, then watch what transpires according to three rules that dictate how the system plays out. Birth rule: An empty, or "dead," cell with precisely three "live" neighbors (full cells) becomes live. Death rule: A live cell with zero or one neighbors dies of isolation; a live cell with four or more neighbors dies of overcrowding. Survival rule: A live cell with two or three neighbors remains alive. With each iteration, some cells live, some die and "Life-forms" evolve, one generation to the next. Among the first creatures to emerge was the glider -- a five-celled organism that moved across the grid with a diagonal wiggle and proved handy for transmitting information. It was discovered by a member of Dr. Conway's research team, Richard Guy, in Cambridge, England. The glider gun, producing a steady stream of gliders, was discovered soon after by Bill Gosper, then at the Massachusetts Institute of Technology.

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hcs_$reboot shares a remarkable new theory from Larry M. Silverberg, an aerospace engineering professor at North Carolina State University (with colleague Jeffrey Eischen). They're proposing that matter is not made of particles (or even waves), as was long thought, but fragments of energy. [W]hile the theories and math of waves and particles allow scientists to make incredibly accurate predictions about the universe, the rules break down at the largest and tiniest scales. Einstein proposed a remedy in his theory of general relativity. Using the mathematical tools available to him at the time, Einstein was able to better explain certain physical phenomena and also resolve a longstanding paradox relating to inertia and gravity. But instead of improving on particles or waves, he eliminated them as he proposed the warping of space and time.Using newer mathematical tools, my colleague and I have demonstrated a new theory that may accurately describe the universe... Instead of basing the theory on the warping of space and time, we considered that there could be a building block that is more fundamental than the particle and the wave.... Much to our surprise, we discovered that there were only a limited number of ways to describe a concentration of energy that flows. Of those, we found just one that works in accordance with our mathematical definition of flow. We named it a fragment of energy... Using the fragment of energy as a building block of matter, we then constructed the math necessary to solve physics problems... More than 100 [years] ago, Einstein had turned to two legendary problems in physics to validate general relativity: the ever-so-slight yearly shift — or precession — in Mercury's orbit, and the tiny bending of light as it passes the Sun... In both problems, we calculated the trajectories of the moving fragments and got the same answers as those predicted by the theory of general relativity. We were stunned. Our initial work demonstrated how a new building block is capable of accurately modeling bodies from the enormous to the minuscule. Where particles and waves break down, the fragment of energy building block held strong. The fragment could be a single potentially universal building block from which to model reality mathematically — and update the way people think about the building blocks of the universe.

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sciencehabit summarizes a new article from Science magazine: Attention racehorse jockeys: Start fast, but save enough energy for a final kick. That's the ideal strategy to win short-distance horse races, according to the first mathematical model to calculate how horses use up energy in races. The researchers say the approach could be used to identify customized pacing plans that, in theory, would optimize individual horses' chances of winning. The team took advantage of a new GPS tracking tool embedded in French racing saddles. The trackers let fans watch digital images of the horses move across a screen, and they gave the researchers real-time speed and position data. The scientists studied patterns in dozens of races at the Chantilly racetracks north of Paris and developed a model that accounted for winning strategies for three different races: a short one (1300 meters), a medium one (1900 meters), and a slightly longer one (2100 meters), all with different starting points on the same curved track. The model takes into account not just different race distances, but also the size and bend of track curves, and any slopes or friction from the track surface. The results might surprise jockeys who hold horses back early for bursts of energy in the last furlough. Instead, a strong start leads to a better finish, the team found. That doesn't mean those jockeys are wrong, though. Too strong of a start can be devastating as well, leaving the horse 'exhausted by the end,' one of the researchers says. Even so, "We can't truly model performance," argues a veterinarian at the University of Sydney with over 30 years of experience working at horse racetracks. But he also asks Science, "Do we really want to? "For people who love horse racing, the uncertainty provides the excitement, and the actual running of the horses provides the spectacle and the beauty."

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Natalie Wolchover writes via Quanta Magazine: As fundamental constants go, the speed of light, c, enjoys all the fame, yet c's numerical value says nothing about nature; it differs depending on whether it's measured in meters per second or miles per hour. The fine-structure constant, by contrast, has no dimensions or units. It's a pure number that shapes the universe to an astonishing degree -- "a magic number that comes to us with no understanding," as Richard Feynman described it. Paul Dirac considered the origin of the number "the most fundamental unsolved problem of physics." Numerically, the fine-structure constant, denoted by the Greek letter a (alpha), comes very close to the ratio 1/137. It commonly appears in formulas governing light and matter. [...] The constant is everywhere because it characterizes the strength of the electromagnetic force affecting charged particles such as electrons and protons. Because 1/137 is small, electromagnetism is weak; as a consequence, charged particles form airy atoms whose electrons orbit at a distance and easily hop away, enabling chemical bonds. On the other hand, the constant is also just big enough: Physicists have argued that if it were something like 1/138, stars would not be able to create carbon, and life as we know it wouldn't exist. Today, in a new paper in the journal Nature, a team of four physicists led by Saida Guellati-Khelifa at the Kastler Brossel Laboratory in Paris reported the most precise measurement yet of the fine-structure constant. The team measured the constant's value to the 11th decimal place, reporting that a = 1/137.03599920611. (The last two digits are uncertain.) With a margin of error of just 81 parts per trillion, the new measurement is nearly three times more precise than the previous best measurement in 2018 by Muller's group at Berkeley, the main competition. (Guellati-Khelifa made the most precise measurement before Muller's in 2011.) Muller said of his rival's new measurement of alpha, "A factor of three is a big deal. Let's not be shy about calling this a big accomplishment."

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AmiMoJo shares a report from the BBC: The winning numbers in South Africa's national lottery have caused a stir and sparked accusations of fraud over their unusual sequence. Tuesday's PowerBall lottery saw the numbers five, six, seven, eight and nine drawn, while the Powerball itself was, you've guessed it, 10. Some South Africans have alleged a scam and an investigation is under way. The organizers said 20 people purchased a winning ticket and won 5.7 million rand ($370,000; 278,000 pounds) each. Another 79 ticketholders won 6,283 rand each for guessing the sequence from five up to nine but missing the PowerBall. The chances of winning South Africa's PowerBall lottery are one in 42,375,200 -- the number of different combinations when selecting five balls from a set of 50, plus an additional bonus ball from a pool of 20. The odds of the draw resulting in the numbers seen in Tuesday's televised live event are the same as any other combination. Competitions resulting in multiple winners are rare, but this may have something to do with this particular sequence.

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A cryptographic master tool called indistinguishability obfuscation has for years seemed too good to be true. Three researchers have figured out that it can work. Erica Klarreich, reporting for Quanta Magazine: In 2018, Aayush Jain, a graduate student at the University of California, Los Angeles, traveled to Japan to give a talk about a powerful cryptographic tool he and his colleagues were developing. As he detailed the team's approach to indistinguishability obfuscation (iO for short), one audience member raised his hand in bewilderment. "But I thought iO doesn't exist?" he said. At the time, such skepticism was widespread. Indistinguishability obfuscation, if it could be built, would be able to hide not just collections of data but the inner workings of a computer program itself, creating a sort of cryptographic master tool from which nearly every other cryptographic protocol could be built. It is "one cryptographic primitive to rule them all," said Boaz Barak of Harvard University. But to many computer scientists, this very power made iO seem too good to be true. Computer scientists set forth candidate versions of iO starting in 2013. But the intense excitement these constructions generated gradually fizzled out, as other researchers figured out how to break their security. As the attacks piled up, "you could see a lot of negative vibes," said Yuval Ishai of the Technion in Haifa, Israel. Researchers wondered, he said, "Who will win: the makers or the breakers?" "There were the people who were the zealots, and they believed in [iO] and kept working on it," said Shafi Goldwasser, director of the Simons Institute for the Theory of Computing at the University of California, Berkeley. But as the years went by, she said, "there was less and less of those people." Now, Jain -- together with Huijia Lin of the University of Washington and Amit Sahai, Jain's adviser at UCLA -- has planted a flag for the makers. In a paper posted online on August 18, the three researchers show for the first time how to build indistinguishability obfuscation using only "standard" security assumptions. All cryptographic protocols rest on assumptions -- some, such as the famous RSA algorithm, depend on the widely held belief that standard computers will never be able to quickly factor the product of two large prime numbers. A cryptographic protocol is only as secure as its assumptions, and previous attempts at iO were built on untested and ultimately shaky foundations. The new protocol, by contrast, depends on security assumptions that have been widely used and studied in the past. "Barring a really surprising development, these assumptions will stand," Ishai said. While the protocol is far from ready to be deployed in real-world applications, from a theoretical standpoint it provides an instant way to build an array of cryptographic tools that were previously out of reach. For instance, it enables the creation of "deniable" encryption, in which you can plausibly convince an attacker that you sent an entirely different message from the one you really sent, and "functional" encryption, in which you can give chosen users different levels of access to perform computations using your data. The new result should definitively silence the iO skeptics, Ishai said. "Now there will no longer be any doubts about the existence of indistinguishability obfuscation," he said. "It seems like a happy end."

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Microsoft is overhauling Excel with the ability to support custom live data types. The Verge reports: You could import the data type for Seattle, for example, and then create a formula that references that single cell to pull out information on the population of Seattle. These data types work by cramming a set of structured data into a single cell in Excel that can then be referenced by the rest of the spreadsheet. Data can also be refreshed to keep it up to date. If you're a student who is researching the periodic table, for example, you could create a cell for each element and easily pull out individual data from there. Microsoft is bringing more than 100 new data types into Excel for Microsoft 365 Personal or Family subscribers. Excel users will be able to track stocks, pull in nutritional information for dieting plans, and much more, thanks to data from Wolfram Alpha's service. This is currently available for Office beta testers in the Insiders program. Where these custom data types will be most powerful is obviously for businesses that rely on Excel daily. Microsoft is leveraging its Power BI service to act as the connector to bring sources of data into Excel data types on the commercial side, allowing businesses to connect up a variety of data. This could be hierarchical data or even references to other data types and images. Businesses will even be able to convert existing cells into linked data types, making data analysis a lot easier. Power BI won't be the only way for this feature to work, though. When you import data into Excel, you can now transform it into a data type with Power Query. That could include information from files, databases, websites, and more. The data that's imported can be cleaned up and then converted into a data type to be used in spreadsheets. If you've pulled in data using Power Query, it's easy to refresh the data from its original source. [...] These new Power BI data types will be available in Excel for Windows for all Microsoft 365 / Office 365 subscribers that also have a Power BI Pro service plan. Power Query data types are also rolling out to subscribers. On the consumer side, Wolfram Alpha data types are currently available in preview for Office insiders and should be available to all Microsoft 365 subscribers soon.

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Tim Harford, writing for Financial Times: A well-designed auction forces bidders to reveal the truth about their own estimate of the prize's value. At the same time, the auction shares that information with the other bidders. And it sets the price accordingly. It is quite a trick. But, in practice, it is a difficult trick to get right. In the 1990s, the US Federal government turned to auction theorists -- Milgrom and Wilson prominent among them -- for advice on auctioning radio-spectrum rights. "The theory that we had in place had only a little bit to do with the problems that they actually faced," Milgrom recalled in an interview in 2007. "But the proposals that were being made by the government were proposals that we were perfectly capable of analysing the flaws in and improving." The basic challenge with radio-spectrum auctions is that many prizes are on offer, and bidders desire only certain combinations. A TV company might want the right to use Band A, or Band B, but not both. Or the right to broadcast in the east of England, but only if they also had the right to broadcast in the west. Such combinatorial auctions are formidably challenging to design, but Milgrom and Wilson got to work. Joshua Gans, a former student of Milgrom's who is now a professor at the University of Toronto, praises both men for their practicality. Their theoretical work is impressive, he said, "but they realised that when the world got too complex, they shouldn't adhere to proving strict theorems."

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After 44 years, there's finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem. From a report: When Nathan Klein started graduate school two years ago, his advisers proposed a modest plan: to work together on one of the most famous, long-standing problems in theoretical computer science. Even if they didn't manage to solve it, they figured, Klein would learn a lot in the process. He went along with the idea. "I didn't know to be intimidated," he said. "I was just a first-year grad student -- I don't know what's going on." Now, in a paper posted online in July, Klein and his advisers at the University of Washington, Anna Karlin and Shayan Oveis Gharan, have finally achieved a goal computer scientists have pursued for nearly half a century: a better way to find approximate solutions to the traveling salesperson problem. This optimization problem, which seeks the shortest (or least expensive) round trip through a collection of cities, has applications ranging from DNA sequencing to ride-sharing logistics. Over the decades, it has inspired many of the most fundamental advances in computer science, helping to illuminate the power of techniques such as linear programming. But researchers have yet to fully explore its possibilities -- and not for want of trying. The traveling salesperson problem "isn't a problem, it's an addiction," as Christos Papadimitriou, a leading expert in computational complexity, is fond of saying. Most computer scientists believe that there is no algorithm that can efficiently find the best solutions for all possible combinations of cities. But in 1976, Nicos Christofides came up with an algorithm that efficiently finds approximate solutions -- round trips that are at most 50% longer than the best round trip. At the time, computer scientists expected that someone would soon improve on Christofides' simple algorithm and come closer to the true solution. But the anticipated progress did not arrive. "A lot of people spent countless hours trying to improve this result," said Amin Saberi of Stanford University. Now Karlin, Klein and Oveis Gharan have proved that an algorithm devised a decade ago beats Christofides' 50% factor, though they were only able to subtract 0.2 billionth of a trillionth of a trillionth of a percent. Yet this minuscule improvement breaks through both a theoretical logjam and a psychological one. Researchers hope that it will open the floodgates to further improvements.

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Long-time Slashdot reader fahrbot-bot shares a story that all started with a high school student's innocuous question on TikTok, leading academic mathematicians and philosophers to weigh in on "a very ancient and unresolved debate in the philosophy of science," reports Smithsonian magazine. "What, exactly, is math?" Is it invented, or discovered? And are the things that mathematicians work with — numbers, algebraic equations, geometry, theorems and so on — real? Some scholars feel very strongly that mathematical truths are "out there," waiting to be discovered — a position known as Platonism.... Many mathematicians seem to support this view. The things they've discovered over the centuries — that there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on forever — seem to be eternal truths, independent of the minds that found them.... Other scholars — especially those working in other branches of science — view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing "outside of space and time" makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago. Platonism, as mathematician Brian Davies has put it, "has more in common with mystical religions than it does with modern science." The fear is that if mathematicians give Plato an inch, he'll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all...? Platonism has various alternatives. One popular view is that mathematics is merely a set of rules, built up from a set of initial assumptions — what mathematicians call axioms... But this view has its own problems. If mathematics is just something we dream up from within our own heads, why should it "fit" so well with what we observe in nature...? Theoretical physicist Eugene Wigner highlighted this issue in a famous 1960 essay titled, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Wigner concluded that the usefulness of mathematics in tackling problems in physics "is a wonderful gift which we neither understand nor deserve."

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Lanodonal writes: A mathematician who tamed a nightmarish family of equations that behave so badly they make no sense has won the most lucrative prize in academia. Martin Hairer, an Austrian-British researcher at Imperial College London, is the winner of the 2021 Breakthrough prize for mathematics, an annual $3m award that has come to rival the Nobels in terms of kudos and prestige. Hairer landed the prize for his work on stochastic analysis, a field that describes how random effects turn the maths of things like stirring a cup of tea, the growth of a forest fire, or the spread of a water droplet that has fallen on a tissue into a fiendishly complex problem. His major work, a 180-page treatise that introduced the world to "regularity structures," so stunned his colleagues that one suggested it must have been transmitted to Hairer by a more intelligent alien civilisation. Hairer, who rents a London flat with his wife and fellow Imperial mathematician, Xue-Mei Li, heard he had won the prize in a Skype call while the UK was still in lockdown. "It was completely unexpected," he said. "I didn't think about it at all, so it was a complete shock. We couldn't go out or anything, so we celebrated at home." The award is one of several Breakthrough prizes announced each year by a foundation set up by the Israeli-Russian investor Yuri Milner and Facebook's Mark Zuckerberg. A committee of previous recipients chooses the winners who are all leading lights in mathematics and the sciences. Other winners announced on Thursday include a Hong Kong scientist, Dennis Lo, who was inspired by a 3D Harry Potter movie to develop a test for genetic mutations in DNA shed by unborn babies, and a team of physicists whose experiments revealed that if extra dimensions of reality exist, they are curled up smaller than a third of a hair's width.

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NCamero (Slashdot reader #35,481) brings some news from the world of 12-sided dodecahedrons: Quanta magazine reports that a trio of mathematicians has resolved one of the most basic questions about the dodecahedron. The cube, tetrahedron, octahedron and icosahedron cannot have a straight path you could take [starting from a corner] that would eventually return you to your starting point without passing through any of the other corners. The dodecahedron can. Mathematicians studied dodecahedrons for over 2,000 years without solving the problem, reports Quanta magazine. But now... Jayadev Athreya, David Aulicino and Patrick Hooper have shown that an infinite number of such paths do in fact exist on the dodecahedron. Their paper, published in May in Experimental Mathematics, shows that these paths can be divided into 31 natural families. The solution required modern techniques and computer algorithms. "Twenty years ago, [this question] was absolutely out of reach; 10 years ago it would require an enormous effort of writing all necessary software, so only now all the factors came together," wrote Anton Zorich, of the Institute of Mathematics of Jussieu in Paris, in an email.

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