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KentuckyFC (1144503) writes "Imagine the following scenario. The end of civilization has occurred, zombies have taken over the Earth and all access to modern technology has ended. The few survivors suddenly need to know the value of pi and, being a mathematician, they turn to you. What do you do? According to a couple of Canadian mathematicians, the answer is to repeatedly fire a Mossberg 500 pump action shotgun at a square aluminum target about 20 meters away. Then imagine that the square is inscribed with an arc drawn between opposite corners that maps out a quarter circle. If the sides of the square are equal to 1, then the area of the quarter circle is pi/4. Next, count the number of pellet holes that fall inside the area of the quarter circle as well as the total number of holes. The ratio between these is an estimate of the ratio between the area of the quarter circle and the area of a square, or in other words pi/4. So multiplying this number by 4 will give you an estimate of pi. That's a process known as a Monte Carlo approximation and it is complicated by factors such as the distribution of the pellets not being random. But the mathematicians show how to handle these too. The result? According to this method, pi is 3.13, which is just 0.33 per cent off the true value. Handy if you find yourself in a post-apocalyptic world."
303 comments | 2 days ago
KentuckyFC writes: "One of the great theories of modern cosmology is that the universe began in a Big Bang. It's backed up by numerous lines of evidence, such as the cosmic microwave background and so on. But what caused the Big Bang, itself? For many years, cosmologists have fallen back on the idea that the universe formed spontaneously; that the Big Bang was result of quantum fluctuations in which the universe came into existence from nothing. But is this compatible with what we know about the Big Bang itself and the theories that describe it? Now cosmologists have come up with the first rigorous proof that the Big Bang could indeed have occurred spontaneously and produced the universe we see today. The proof is developed within a mathematical framework known as the Wheeler-DeWitt equation. Heisenberg's uncertainty principle allows a small region of empty space to come into existence probabilistically due to quantum fluctuations. Most of the time, such a bubble will collapse and disappear. The question these scientists address is whether a bubble could also expand exponentially to allow a universe to form in an irreversible way. Their proof (PDF) shows that this is indeed possible. There is an interesting corollary: the role of the cosmological constant is played by a property known as the quantum potential. This is a property introduced in the 20th century by the physicist David Bohm, which has the effect of making quantum mechanics deterministic while reproducing all of its predictions. It's an idea that has never caught on. Perhaps that will change now."
589 comments | 4 days ago
An anonymous reader writes "When the Obama administration announced on April 1 that an estimated 7.1 million had signed up for ObamaCare by the end of March, it seemed a nearly impossible achievement. To reach 7.1 million, sign-ups had to rocket up by 67% in just one month. That's astounding enough, but an IBD review of existing ObamaCare enrollment data shows that the mathematical challenge of reaching 7.1 million sign-ups was even tougher."
719 comments | 5 days ago
Martin S. (98249) writes "The Register reports on a paper at the arXiv (abstract below) by Christian Decker and Roger Wattenhofer analyzing a year's worth of Bitcoin activity to reach the conclusion that MtGox's claims of losing their bitcoins because of the transaction malleability bug are untrue. The Abstract claims: 'In Bitcoin, transaction malleability describes the fact that the signatures that prove the ownership of bitcoins being transferred in a transaction do not provide any integrity guarantee for the signatures themselves. ... In this work we use traces of the Bitcoin network for over a year preceding the filing to show that, while the problem is real, there was no widespread use of malleability attacks before the closure of MtGox.'" Quoting El Reg: "By extracting transaction keys from the transaction set, the researchers say, they were able to identify more than 35,000 transaction conflicts and more than 29,000 “confirmed attacks” covering more than 300,000 Bitcoins." And less than 6000 were actually successful.
92 comments | about a week ago
mikejuk (1801200) writes "The Matrix Reloaded started something when 'The Merovingian' wore a number of very flashy ties. The problem was that we thought we knew how many ways you can tie a tie. The number of ways had been enumerated in 2001 and the answer was that there were exactly 85 different ways but the enumeration didn't include the Matrix way of doing it. So how many "Merovingian" knots are there? The question is answered in a new paper, More ties than we thought [PDf], by Dan Hirsch, Meredith L. Patterson, Anders Sandberg and Mikael Vejdemo-Johansson. The methodology is based on the original enumeration and an interesting application of language theory. The idea is to create a programming language for tying ties and then work out how many programs there are. For single depth tucks there are 177,147 different sequences and hence knots. Of these there are 2046 winding patterns that take up to 11 moves, the same as the The Merovingian knot and other popular knots, and so these are probably practical with a normal length necktie."
51 comments | about two weeks ago
New submitter arsheive (609065) writes with a link to this interesting RPS brainteaser: "How do you play against an opponent who _must_ throw Rock 50% of the time, and how much would you be willing to pay to play against them?"
167 comments | about two weeks ago
xyourfacekillerx writes "Not long ago, Slashdot readers answered a question for someone seeking to finish a BS in CS online. I am in a similar situation with a different question. I have spent five years frivolously studying philosophy at a very expensive university, and now I want to start towards an Associate's in CS, and then perhaps a Bachelor's (I want to program for a living; I write code daily anyways). After four hours of combing through Google results, I still don't have much useful information. Problem 1: I am out of money and I have an 8 to 5 job, so on-campus enrollment is not an option. Problem 2: and I have very little to transfer due to the specificity of my prior studies: I don't even have my core English/Language or even math cores to transfer. My questions are: 1) Just where are the open CS courses? Who offers it in a way that's more than just lecture notes posts online? 2) Can any of it help or hinder me getting a degree (i.e. does any of it transfer, potentially? Is it a waste of time? Additionally, any tips about accredited online universities (preferably self-paced) where I can start to get my associates and/or bachelor's in CS at low cost would be useful. I intend to be enrolled online somewhere by Fall, and I am starting my own search among local (Colorado) junior colleges who don't demand on-campus presence like most four-years schools do."
84 comments | about two weeks ago
KentuckyFC writes: "One of the greatest mysteries in science is why we don't see quantum effects on the macroscopic scale; why Schrodinger's famous cat cannot be both alive and dead at the same time. Now one theorist says the answer is because P is NOT equal to NP. Here's the thinking: The equation that describes the state of any quantum object is called Schrodinger's equation. Physicists have always thought it can be used to describe everything in the universe, even large objects, and perhaps the universe itself. But the new idea is that this requires an additional assumption — that an efficient algorithm exists to solve the equation for complex macroscopic systems. But is this true? The new approach involves showing that the problem of solving Schrodinger's equation is NP-hard. So if macroscopic superpositions exist, there must be an algorithm that can solve this NP-hard problem quickly and efficiently. And because all NP-hard problems are mathematically equivalent, this algorithm must also be capable of solving all other NP-hard problems too, such as the traveling salesman problem. In other words, NP-hard problems are equivalent to the class of much easier problems called P. Or P=NP. But here's the thing: computational complexity theorists have good reason to think that P is not equal to NP (although they haven't yet proven it). If they're right, then macroscopic superpositions cannot exist, which explains why we do not (and cannot) observe them in the real world. Voila!"
199 comments | about two weeks ago
KentuckyFC (1144503) writes "The question of what makes puzzles hard for humans is deceptively tricky. One possibility is that puzzles that are hard for computers must also be hard for people. That's undoubtedly true and in recent years computational complexity theorists have spent some time trying to classify the games people play in this way (Pac Man is NP hard, by the way). But humans don't always solve problems in the same way as computers because they don't necessarily pick the best method or even a good way to do it. And that makes it hard to predict the difficulty of a puzzle in advance. Cognitive psychologists have attempted to tease this apart by measuring how long it takes people to solve puzzles and then creating a model of the problem solving process that explains the data.
But the datasets gathered in this way have been tiny — typically 20 people playing a handful of puzzles. Now one researcher has taken a different approach by mining the data from websites in which people can play games such as Sudoku. That's given him data on the way hundreds of players solve over 2000 puzzles, a vast increase over previous datasets and this has allowed him to plot the average time it takes to finish different puzzles. One way to assess the difficulty of Sudoku puzzle is in the complexity of each step required to solve it. But the new work suggests that another factor is important too — whether the steps are independent and so can be attempted in parallel or whether the steps are dependent and so must be tried in sequence, one after the other. A new model of this puzzle-solving process accurately reproduces the time it takes real humans to finish the problems and that makes it possible to accurately predict the difficulty of a puzzle in advance for the first time. It also opens the way for other studies of human problem solving using the vast datasets that have been collected over the web. Indeed work has already begun on the Sudoku-like puzzle game, Nurikabe."
44 comments | about two weeks ago
New submitter Mark Buchanan (3595113) writes with a story about research from scientists at MIT, Cornell and elsewhere showing "that big city taxi systems could be made 40% more efficient with device-enabled taxi sharing. We could cut miles driven, costs, and pollution with the right application of just data and algorithms, and do it while introducing no more than a 5 minute delay to any person's trip. " Letting such algorithms compete seems an excellent reason to encourage, rather than reject by law, ride-coordination services like Uber and Lyft.
72 comments | about three weeks ago
mdsolar (1045926) writes "Malaysian Prime Minister Najib Razak has announced that, based on satellite data analysis from UK company Inmarsat, Malayian Airlines flight MH370 ended in the southern Indian Ocean, and no one on board survived. 'Effectually we looked at the doppler effect, which is the change in frequency, due to the movement of a satellite in its orbit. What that then gave us was a predicted path for the northerly route and a predicted path the southerly route,' explained Chris McLaughlin, senior vice president of external affairs at Inmarsat. 'What we discovered was a correlation with the southerly route and not with the northern route after the final turn that the aircraft made, so we could be as close to certain as anybody could be in that situation that it went south. Where we then went was to work out where the last ping was, knowing that the aircraft still had some fuel, but that it would have run out before the next automated ping. We don't know what speed the aircraft was flying at, but we assumed about 450 knots.' Inmarsat passed the relevant analysis to the UK Air Accidents Investigation Branch (AAIB) yesterday. The cause of the crash remains a mystery."
491 comments | about three weeks ago
mdsolar (1045926) writes with this excerpt from Slate on the still-missing Malaysian Airline flight "In a case that is swirling with uncertainties, a few pieces of evidence have stood apart for seeming reliability. Among them was the revelation last Saturday by Malaysia Prime Minister Najib Razak that his country's investigators, in collaboration with U.S. authorities, had analyzed an electronic ping that MH370 had broadcast to the Inmarsat satellite at 8:11 a.m. on the morning of the disappearance. Based on this data, the investigators had determined that at that moment MH370 must have been somewhere along one of two broad arcs: one which passed through Central Asia, and the other of which covered a swath of largely empty Indian Ocean, far to the south. The revelation left a burning question unresolved: what about the six earlier pings, which had been exchanged between the aircraft and the satellite about once per hour? Could any position data be deduced from them? Today, Inmarsat revealed some crucial information. 'The ping timings got longer,' Inmarsat spokesman Chris McLaughlin stated via email. That is to say, at each stage of its journey, the aircraft got progressively farther away from the geostationary satellite's position, located over a spot on the equator south of Pakistan, and never changed its heading in a direction that took it closer—at least for very long."
227 comments | about three weeks ago
Hugh Pickens DOT Com (2995471) writes "Jake Simpson reports at The Atlantic that Mathematician Tim Chartier, a Davidson College professor who specializes in ranking methods, teaches a math-heavy form of bracketology — the science of predicting the annual NCAA college basketball tournament at Davidson College in North Carolina. Chartier's academic research is in ranking methods where he looks at things like the page-ranking algorithms of Google. 'In 2009, my collaborator Amy Langville said: "You know what? ESPN has this huge online bracket tournament. Let's create brackets with our ranking methods, just to see if it's creating meaningful information."' Chartier's formula, an evolving code-based matrix that ranks each of the 68 tournament teams, has helped several Davidson students score in the 96th percentile (or higher) in ESPN's bracket challenge and this year, Chartier's goal is to help someone win the $1 billion prize offered by Warren Buffett to anyone who correctly predicts all 63 games of the men's tournament.
Chartier uses two methods. One is the Colley Method, named after astrophysicist Wesley Colley who developed a method used by the BCS for college football (PDF). His basketball method only counts wins and losses, not margin of victory. The other method is the Massey method created by sports statistician Kenneth Massey (PDF), which does integrate scores. Chartier has not been banned from any office pools — at least none that he knows of. But as a result of coming pretty darn close to filling out a perfect bracket just by crunching the numbers, brackets have become a labor of love. 'Now that the brackets are actually out, I've had students in and out of my office all week, sharing new ideas,' says Chartier. 'For me, that's more fun than filling out a bracket. They will all be filling out brackets, so it's like I'm doing parallel processing. I know what might work, but watching them figure out the odds, is a thrill.'"
76 comments | about a month ago
mikejuk writes to let us know that today is Pi Day — 3/14 in American date notation. He writes, "This year, it feels as though we aren't celebrating alone. For the first time, it looks as if momentum has built up to the point where people have heard about Pi Day. There are even attempts to sell you Pi-related items as if it was a real holiday. But there is always some one to spoil the party so what ever you do to celebrate don't miss Vi Hart's Anti-Pi Rant video." Thus begins the yearly debate over Pi Day vs. Tau Day (June 28). Phil Plait has a post defending Pi Day's honor, and MIT isn't holding back their Pi Day celebrations.
218 comments | about a month ago
theodp writes "'I want to explain why Common Core is among the most important education ideas in years,' wrote Bill Gates in a USA Today op-ed last month that challenged the "dangerous misconceptions" of those who oppose the initiative (pretty confident for a guy who conceded there wasn't much to show for his earlier $5B education reform effort!). 'The Gates Foundation helped fund this process,' acknowledged Gates in quite an understatement of his influence. Receiving $6.5M in Gates Grants was Student Achievement Partners, whose founder David Coleman was dubbed the 'Architect of the Common Core.' So it's not too surprising that at last week's SXSWedu, Coleman — now President and CEO of The College Board (no stranger to Gates money itself) — announced a dramatic overhaul of the SAT that includes a new emphasis on evidence-based reading and writing and evidence analysis, which the AJC's Maureen Downey calls 'reflective of the approach of the Common Core State Standards.'" (Read more, below.)
273 comments | about a month ago
sciencehabit writes "Think women can't do math? You're wrong — but new research (paywalled) shows you might not change your mind, even if you get evidence to the contrary. A study of how both men and women perceive each other's mathematical ability finds that an unconscious bias against women — by both men and women — could be skewing hiring decisions, widening the gender gap in mathematical professions like engineering."
384 comments | about a month ago
An anonymous reader writes "I am a middle school math teacher and I also run a programming club. I recent completed my M.Ed in math education and was inspired to try to do the new GT online MS in Computer Science in a couple of years. I have some background in programming: two intro to comp sci courses, Java, C++, Python, the main scripting languages, and a bunch of math background. I also read through this great article on getting these pre-requisites completed through Coursera but unfortunately you need to wait for courses to enroll. I would like to just learn these on my own time, no credit necessary. Suggestions?"
197 comments | about a month ago
cartechboy writes "Math watch time: For many traffic analysts, INRIX is considered the gold-standard. This week the company says traffic congestion surged in 2013 and grew over three times as fast as the American economy. The bad news: If true, this reverses two consecutive years of traffic declines with a six percent increase in 2013. (GDP, by comparison, grew 1.9 percent last year.) The analysts then theorize links between economic growth and traffic congestion, which makes sense on the surface. (As the economy improves, more jobs are created, so more commuters on the roads) But INRIX's theory creates as many questions as it answers. For example, the U.S. GDP has been steadily growing since 2009. So why did congestion decline in 2011 and 2012?"
187 comments | about a month ago
An anonymous reader writes "According to the NY Times, 'Saying its college admission exams do not focus enough on the important academic skills, the College Board announced on Wednesday a fundamental rethinking of the SAT, eliminating obligatory essays, ending the longstanding penalty for guessing wrong and cutting obscure vocabulary words. ... The SAT's rarefied vocabulary words will be replaced by words that are common in college courses, such as "empirical" and "synthesis." The math questions, now scattered widely across many topics, will focus more narrowly on linear equations, functions and proportional thinking. The use of a calculator will no longer be allowed on some of the math sections.' The College Board will also be working with Khan Academy to provide students with free, online practice problems and instructional videos. The new version of the SAT will be introduced in 2016."
134 comments | about a month ago
An anonymous reader writes "Mathematics Ph.D. student Jeremy Kun has an interesting post about how mathematicians approach doing new work and pushing back the boundaries of human knowledge. He says it's immensely important for mathematicians to be comfortable with extended periods of ignorance when working on a new topic. 'The truth is that mathematicians are chronically lost and confused. It's our natural state of being, and I mean that in a good way. ... This is something that has been bred into me after years of studying mathematics. I know how to say, “Well, I understand nothing about anything,” and then constructively answer the question, “What’s next?” Sometimes the answer is to pinpoint one very basic question I don’t understand and try to tackle that first.' He then provides some advice for people learning college level math like calculus or linear algebra: 'I suggest you don't worry too much about verifying every claim and doing every exercise. If it takes you more than 5 or 10 minutes to verify a "trivial" claim in the text, then you can accept it and move on. ... But more often than not you'll find that by the time you revisit a problem you've literally grown so much (mathematically) that it's trivial. What's much more useful is recording what the deep insights are, and storing them for recollection later.'"
114 comments | about a month ago
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