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Mathematicians Protest Russia Hosting Major Conference

著者: msmash
2022年3月3日 07:43
As Ukrainian researchers have feared for their lives and careers after Russia's invasion of Ukraine, mathematicians have been grappling over what to do about a prominent mathematical conference that was set to be held in Saint Petersburg, Russia, in July. From a report: The International Congress of Mathematicians (ICM) is "the largest and most significant conference on pure and applied mathematics as well as one of the world's oldest scientific congresses," according to the Web site of the 2022 conference. The meeting, which is run by the Germany-based International Mathematical Union (IMU), is held only once every four years. When the nine-day 2018 ICM was held in Rio de Janeiro, Brazil, it drew 10,506 attendees. On Saturday conference organizers announced the event would be fully virtual and hosted outside of Russia this year. The executive committee of the meeting released a statement saying, "We strongly condemn the actions by Russia. Our deepest sympathy goes to our Ukrainian colleagues and the Ukrainian people. Given this situation, it is impossible for the IMU to host the ICM and the GA [general assembly] as traditional in-person events in Russia." The Fields Medal -- one of the most prestigious honors in mathematics -- is traditionally awarded at the event. According to the recent decision, this year's prize ceremony and general assembly will be held in person but at an undecided location outside of Russia.

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Children May Instinctively Know How To Do Division Even Before Hitting the Books, Study Finds

著者: msmash
2022年2月26日 06:25
An anonymous reader shares a report: We often think of multiplication and division as calculations that need to be taught in school. But a large body of research suggests that, even before children begin formal education, they possess intuitive arithmetic abilities. A new study published in Frontiers in Human Neuroscience argues that this ability to do approximate calculations even extends to that most dreaded basic math problem -- true division -- with implications for how students are taught mathematical concepts in the future. The foundation for the study is the approximate number system (ANS), a well-established theory that says people (and even nonhuman primates) from an early age have an intuitive ability to compare and estimate large sets of objects without relying upon language or symbols. For instance, under this non-symbolic system, a child can recognize that a group of 20 dots is bigger than a group of four dots, even when the four dots take up more space on a page. The ability to make finer approximations -- say, 20 dots versus 17 dots -- improves into adulthood.

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Harvard Mathematician Proves 150-Year Old Chess Puzzle

著者: BeauHD
2022年2月15日 09:39
joshuark shares a report from Popular Mechanics: A mathematician from Harvard University has (mostly) solved a 150-year-old Queen's gambit of sorts: the delightful n queens puzzle. In newly self-published research (meaning it has not yet been peer-reviewed), Michael Simkin, a postdoctoral fellow at Harvard's Center of Mathematical Sciences and Applications, estimated the solution to the thorny math problem, which is based loosely on the rules of chess. The queen is largely understood to be the most powerful piece on the board because she can move in any direction, including diagonals. So how many queens can fit on the chess board without falling into each other's paths? The logic at play here is similar to a sudoku puzzle, dotting queens on the board so that they don't intersect. Picture a classic chess board, which is an eight-by-eight matrix of squares. The most well-known version of the puzzle matches the board because it involves eight queens -- and there are 92 solutions in this case. But the "n queens problem" doesn't stop there; that's because its nature is asymptotic, meaning its answers approach an undefined value that reaches for the infinite. Up until now, experts have explicitly solved for all the natural numbers (the counting numbers) up to 27 queens in a 27-by-27 board. However, there is no solution for two or three, because there's no possible positioning of queens that satisfies the criteria. But what about numbers above 27? Consider this: for eight queens, there are just 92 solutions, but for 27 queens, there are over 200 quadrillion solutions. It's easy to see how solving the problem for numbers higher than 27 becomes extremely unwieldy or even impossible without more computing power than we have at the moment. That's where Simkin's work enters the arena. His work approached the topic through a sharp mathematical estimate of the number of solutions as n increases. Ultimately, he arrived at the following formula: (0.143n)n. In other words, there are approximately (0.143n)n ways that you can place the queens so that none are attacking one another on an n-by-n chessboard.

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Researchers Use Tiny Magnetic Swirls To Generate True Random Numbers

著者: BeauHD
2022年2月9日 19:00
A group of Brown University physicists has developed a technique that can potentially generate millions of random digits per second by harnessing the behavior of skyrmions -- tiny magnetic anomalies that arise in certain two-dimensional materials. Phys.Org reports: Their research, published in Nature Communications, reveals previously unexplored dynamics of single skyrmions, the researchers say. Discovered around a half-decade ago, skyrmions have sparked interest in physics as a path toward next-generation computing devices that take advantage of the magnetic properties of particles -- a field known as spintronics. [...] Skyrmions arise from the "spin" of electrons in ultra-thin materials. Spin can be thought of as the tiny magnetic moment of each electron, which points up, down or somewhere in between. Some two-dimensional materials, in their lowest energy states, have a property called perpendicular magnetic anisotropy -- meaning the spins of electrons all point in a direction perpendicular to the film. When these materials are excited with electricity or a magnetic field, some of the electron spins flip as the energy of the system rises. When that happens, the spins of surrounding electrons are perturbed to some extent, forming a magnetic whirlpool surrounding the flipped electron -- a skyrmion. Skyrmions, which are generally about 1 micrometer (a millionth of a meter) or smaller in diameter, behave a bit like a kind of particle, zipping across the material from side to side. And once they're formed, they're very difficult to get rid of. Because they're so robust, researchers are interested in using their movement to perform computations and to store data. This new study shows that in addition to the global movement of skyrmions across a material, the local behavior of individual skyrmions can also be useful. For the study, which was led by Brown postdoctoral fellow Kang Wang, the researchers fabricated magnetic thin films using a technique that produced subtle defects in the material's atomic lattice. When skyrmions form in the material, these defects, which the researchers call pinning centers, hold the skyrmions firmly in place rather than allowing them to move as they normally would. The researchers found that when a skyrmion is held in place, they fluctuate randomly in size. With one section of the skyrmion held tightly to one pinning center, the rest of the skyrmion jumps back and forth, wrapping around two nearby pinning centers, one closer and one farther away. The change in skyrmion size is measured through what's known as the anomalous Hall effect, which is a voltage that propagates across the material. This voltage is sensitive to the perpendicular component of electron spins. When the skyrmion size changes, the voltage changes to an extent that is easily measured. Those random voltage changes can be used to produce a string of random digits. The researchers estimate that by optimizing the defect-spacing in their device, they can produce as many as 10 million random digits per second, providing a new and highly efficient method of producing true random numbers.

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A Conway 'Game of Life' Conjecture Settled After 29 years

著者: EditorDavid
2022年1月24日 00:34
In 1992 John Conway raised a question about the patterns in his famous mathematical Game of Life: "Is there a Godlike still-life, one that can only have existed for all time (apart from things that don't interfere with it)?" Conway closed his note by adding "Well, I'm going out to get a hot dog now..." And then, nearly 30 years later, a mathematical blog reports: Ilkka Törmä and Ville Salo, a pair of researchers at the University of Turku in Finland, have found a finite configuration in Conway's Game of Life such that, if it occurs within a universe at time T, it must have existed in that same position at time T-1 (and therefore, by induction, at time 0)... The configuration was discovered by experimenting with finite patches of repeating 'agar' and using a SAT solver to check whether any of them possess this property. The blogger also shares some other Game of Life-related news: David Raucci discovered the first oscillator of period 38. The remaining unsolved periods are 19, 34, and 41.Darren Li has connected Charity Engine to Catagolue, providing approximately 2000 CPU cores of continuous effort and searching slightly more than 10^12 random initial configurations per day.Nathaniel Johnston and Dave Greene have published a book on Conway's Game of Life, featuring both the theoretical aspects and engineering that's been accomplished in the half-century since its conception. Unfortunately it was released slightly too early to include the Törmä-Salo result or Raucci's period-38 oscillator. Thanks to Slashdot reader joshuark for sharing the story.

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Mathematician Hurls Structure and Disorder Into Century-Old Problem

著者: msmash
2021年12月16日 23:42
How many red and blue beads can you string together without making a big evenly spaced sequence of the same color? Using a semi-structured pattern of squashed circles, a mathematician shattered the previous record for how long you can keep stringing beads. From a report: The mathematician Ben Green of the University of Oxford has made a major stride toward understanding a nearly 100-year-old combinatorics problem, showing that a well-known recent conjecture is "not only wrong but spectacularly wrong," as Andrew Granville of the University of Montreal put it. The new paper shows how to create much longer disordered strings of colored beads than mathematicians had thought possible, extending a line of work from the 1940s that has found applications in many areas of computer science. The conjecture, formulated about 17 years ago by Ron Graham, one of the leading discrete mathematicians of the past half-century, concerns how many red and blue beads you can string together without creating any long sequences of evenly spaced beads of a single color. (You get to decide what "long" means for each color.) This problem is one of the oldest in Ramsey theory, which asks how large various mathematical objects can grow before pockets of order must emerge. The bead-stringing question is easy to state but deceptively difficult: For long strings there are just too many bead arrangements to try one by one.

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'When a Newspaper Publishes an Unsolvable Puzzle'

著者: EditorDavid
2021年12月13日 00:34
Slashdot reader DevNull127 writes: It's a newspaper puzzle that's like Sudoku, except it's impossible. [Sort of...] They call it "The Challenger" puzzle — but when the newspaper leaves out a crucial instruction, you can end up searching forever for a unique solution which doesn't exist! "If you're thinking 'This could be a 9 or an 8....' — you're right!" complains Lou Cabron. "Everyone's a winner today! Just start scribbling in numbers! And you'd be a fool to try to keep narrowing them down by, say, using your math and logic skills. A fool like me..." (Albeit a fool who once solved a Sudoku puzzle entirely in his head.) But two hours of frustration later — and one night of bad dreams — he's stumbled onto the web page of Dr. Robert J. Lopez, an emeritus math professor in Indiana, who's calculated that in fact Challenger puzzles can have up to 190 solutions... and there's more than one solution for more than 97% of them! At the end of the day, it becomes an appreciation for the local newspaper, and the puzzles they run next to the funnies. But with a friendly reminder "that they ought to honor and respect that love — by always providing the complete instructions."

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Researchers Claim Locally-Testable-Code Breakthrough With Exotic Multi-Dimensional Graph

著者: EditorDavid
2021年11月29日 01:34
"A team of researchers has finally created a long-sought locally testable code that can immediately betray whether it's been corrupted..." reports Quanta magazine. "Many thought local testability would never be achieved in its ideal form." Now, in a preprint released on November 8, the computer scientist Irit Dinur of the Weizmann Institute of Science and four mathematicians, Shai Evra, Ron Livne, Alex Lubotzky and Shahar Mozes, all at the Hebrew University of Jerusalem, have found it. "It's one of the most remarkable phenomena that I know of in mathematics or computer science," said Tom Gur of the University of Warwick. "It's been the holy grail of an entire field." Their new technique transforms a message into a super-canary, an object that testifies to its health better than any other message yet known. Any corruption of significance that is buried anywhere in its superstructure becomes apparent from simple tests at a few spots. "This is not something that seems plausible," said Madhu Sudan of Harvard University. "This result suddenly says you can do it." Most prior methods for encoding data relied on randomness in some form. But for local testability, randomness could not help. Instead, the researchers had to devise a highly nonrandom graph structure entirely new to mathematics, which they based their new method on. It is both a theoretical curiosity and a practical advance in making information as resilient as possible.... To get a sense of what their graph looks like, imagine observing it from the inside, standing on a single edge. They construct their graph such that every edge has a fixed number of squares attached. Therefore, from your vantage point you'd feel as if you were looking out from the spine of a booklet. However, from the other three sides of the booklet's pages, you'd see the spines of new booklets branching from them as well. Booklets would keep branching out from each edge ad infinitum. "It's impossible to visualize. That's the whole point," said Lubotzky. "That's why it is so sophisticated...." [A] test at one node can reveal information about errors from far away nodes. By making use of higher dimensions, the graph is ultimately connected in ways that go beyond what we typically even think of as connections... It establishes a new state of the art for error-correcting codes, and it also marks the first substantial payoff from bringing the mathematics of high-dimensional expanders to bear on codes... Practical and theoretical applications should soon follow. Different forms of locally testable codes are now being used in decentralized finance, and an optimal version will allow even better decentralized tools.

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Mathematical Model Predicts Best Way To Build Muscle

著者: BeauHD
2021年8月24日 12:30
An anonymous reader quotes a report from Phys.Org: Researchers have developed a mathematical model that can predict the optimum exercise regime for building muscle. The researchers, from the University of Cambridge, used methods of theoretical biophysics to construct the model, which can tell how much a specific amount of exertion will cause a muscle to grow and how long it will take. The model could form the basis of a software product, where users could optimize their exercise regimes by entering a few details of their individual physiology. The results, reported in the Biophysical Journal, suggest that there is an optimal weight at which to do resistance training for each person and each muscle growth target. Muscles can only be near their maximal load for a very short time, and it is the load integrated over time which activates the cell signaling pathway that leads to synthesis of new muscle proteins. But below a certain value, the load is insufficient to cause much signaling, and exercise time would have to increase exponentially to compensate. The value of this critical load is likely to depend on the particular physiology of the individual. In 2018, the Cambridge researchers started a project on how the proteins in muscle filaments change under force. They found that main muscle constituents, actin and myosin, lack binding sites for signaling molecules, so it had to be the third-most abundant muscle component -- titin -- that was responsible for signaling the changes in applied force. Whenever part of a molecule is under tension for a sufficiently long time, it toggles into a different state, exposing a previously hidden region. If this region can then bind to a small molecule involved in cell signaling, it activates that molecule, generating a chemical signal chain. Titin is a giant protein, a large part of which is extended when a muscle is stretched, but a small part of the molecule is also under tension during muscle contraction. This part of titin contains the so-called titin kinase domain, which is the one that generates the chemical signal that affects muscle growth. The molecule will be more likely to open if it is under more force, or when kept under the same force for longer. Both conditions will increase the number of activated signaling molecules. These molecules then induce the synthesis of more messenger RNA, leading to production of new muscle proteins, and the cross-section of the muscle cell increases. This realization led to the current work. [The researchers] set out to constrict a mathematical model that could give quantitative predictions on muscle growth. They started with a simple model that kept track of titin molecules opening under force and starting the signaling cascade. They used microscopy data to determine the force-dependent probability that a titin kinase unit would open or close under force and activate a signaling molecule. They then made the model more complex by including additional information, such as metabolic energy exchange, as well as repetition length and recovery. The model was validated using past long-term studies on muscle hypertrophy. "Our model offers a physiological basis for the idea that muscle growth mainly occurs at 70% of the maximum load, which is the idea behind resistance training," said [one of the paper's authors]. "Below that, the opening rate of titin kinase drops precipitously and precludes mechanosensitive signaling from taking place. Above that, rapid exhaustion prevents a good outcome, which our model has quantitatively predicted." [...] The model also addresses the problem of muscle atrophy, which occurs during long periods of bed rest or for astronauts in microgravity, showing both how long can a muscle afford to remain inactive before starting to deteriorate, and what the optimal recovery regime could be.

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Scientists Calculate Pi To 62.8 Trillion Digits

著者: msmash
2021年8月18日 05:05
OneHundredAndTen writes: Pi is now known to 62.8 trillion decimal digits. Motherboard adds: Researchers in Switzerland broke the world record for the most accurate value of pi over the weekend, the team announced on Monday. They calculated the first 62.8 trillion digits, surpassing the former record by 12.8 trillion decimal points. Calculation first started in late April at the Competence Center for Data Analysis, Visualization and Simulation (DAViS) at the University of Applied Sciences in Graubünden, Switzerland. The calculated data was then backed up onto the high-performance computer where a Y-cruncher wrote it into the hexadecimal notation. It was then converted into the decimal system and verified by a mathematical algorithm

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Ask Slashdot: Is There a 'Standard' Way of Formatting Numbers?

著者: EditorDavid
2021年8月15日 00:34
Long-time Slashdot reader Pieroxy is working on a new open source project, a web-based version of the system-monitoring software Conky. The ultimate goal is send the data to an HTML interface "to find some use for the old iPads/tablets/laptops we all have lying around. You can put them next to your screen and have your metrics displayed there...!" There's just one problem: "I had to come up with a way for users to format a number." I needed a small string the user could write to describe exactly what they want to do with their number. Some examples can be: write it as a 3-digit number suffixed by SI prefixes when the numbers are too big or too small, display a timestamp as HH:MM string, or just the day of week, eventually cut to the first three characters, do the same with a timestamp in milliseconds, or nanoseconds, display a nice string out of a number of seconds to express a duration ("3h 12mn 17s"), pad the number with spaces so that all numbers are aligned (left or right), force a fixed number of digits after the decimal point, etc. In other words, I was looking for a "universal" way of formatting numbers and failed to find any kind of standard online. Do Slashdot readers know of such a thing or should I create my own?

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Australian Mathematician Discovers Applied Geometry Engraved on 3,700-year-old Tablet

著者: msmash
2021年8月5日 02:21
An Australian mathematician has discovered what may be the oldest known example of applied geometry, on a 3,700-year-old Babylonian clay tablet. Known as Si.427, the tablet bears a field plan measuring the boundaries of some land. From a report: The tablet dates from the Old Babylonian period between 1900 and 1600 BCE and was discovered in the late 19th century in what is now Iraq. It had been housed in the Istanbul Archaeological Museum before Dr Daniel Mansfield from the University of New South Wales tracked it down. Mansfield and Norman Wildberger, an associate professor at UNSW, had previously identified another Babylonian tablet as containing the world's oldest and most accurate trigonometric table. At the time, they speculated the tablet was likely to have had some practical use, possibly in surveying or construction. That tablet, Plimpton 322, described right-angle triangles using Pythagorean triples: three whole numbers in which the sum of the squares of the first two equals the square of the third -- for example, 3^2 + 4^2 = 5^2.

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When Graphs Are a Matter of Life and Death

著者: msmash
2021年6月17日 20:00
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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Adding Is Favored Over Subtracting In Problem Solving

著者: BeauHD
2021年4月9日 11:02
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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Quantum Computer Solves Decades-Old Problem Three Million Times Faster Than a Classical Computer

著者: EditorDavid
2021年2月28日 03:34
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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Machines Are Inventing New Math We've Never Seen

著者: BeauHD
2021年2月11日 06:25
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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Hitchhiker's Guide To the Galaxy: New Research Says #42 Really Is Our Number

著者: EditorDavid
2021年2月1日 02:34
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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Quixotic Californian Crusade To Officially Recognize the Hellabyte

著者: BeauHD
2021年1月16日 22:00
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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The Lasting Lessons of John Conway's Game of Life

著者: msmash
2020年12月29日 18:00
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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