An anonymous reader writes: A recent paper from the University of Illinois at Urbana-Champaign shows that bitcoin mining profits can be increased considerably if mining hardware is allowed to produce occasional errors. The research shows that mining hardware that allows occasional errors ("approximate mining") can run much faster and take up less area than a conventional miner. Furthermore, the errors that are produced by the miner do no corrupt the blockchain since such errors are easily detected and discarded by the bitcoin network. Mining profits can increase by over 30%.

Flash Modin writes: In 1936, twenty years after Albert Einstein introduced the concept, the great physicist took another look at his math and came to a surprising conclusion. 'Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation,' he wrote in a letter to friend Max Born. Interestingly, his research denouncing gravitational waves was rejected by Physical Review Letters, the journal that just published proof of their existence. The story shows that even when Einstein's wrong, it's because he was already right the first time.

Andy Nicholls has been an R programmer and consultant for Mango Solutions since 2011 (where he currently manages the R consultancy team), after a long stint as a statistician in the pharmaceutical industry. He has a serious background in mathematics, too, with a Masters in math and another in Statistics with Applications in Medicine. Andy has taught more than 50 on-site R training courses and has been involved in the development of more than 30 R packages; he's also a regular contributor to events at LondonR, the largest R user group in the UK. But since not everyone can get to London for a user group meeting, you can get some of the insights he's gained as an R expert in Sams Teach Yourself R In 24 Hours (available in print or at Safari), of which he is the lead author. Today, though, you can ask Andy about the much-lauded statistics-oriented free software (GPL) language directly -- Why to use it, how to get started, how to get things done, and where those intriguing release names come from. (The about page is helpful, too.) As usual, please ask as many questions as you'd like, but one question at a time, please.

AthanasiusKircher writes: The Atlantic has an >extended article on the recent surge in advanced math education at the primary and secondary levels in the U.S., arguing that last year's victory for the U.S. in the Math Olympiad was not a random anomaly. Participation in math camps, after-school or weekend math "academies," and math competitions has surged in recent years, with many programs having long wait lists. Inessa Rifkin, co-founder of one of these math academies, argues that the problems with math education begin in the 2nd and 3rd grades: ""The youngest ones, very naturally, their minds see math differently.... It is common that they can ask simple questions and then, in the next minute, a very complicated one. But if the teacher doesn't know enough mathematics, she will answer the simple question and shut down the other, more difficult one." These alternative math programs put a greater focus on problem-solving: "Unlike most math classes, where teachers struggle to impart knowledge to students—who must passively absorb it and then regurgitate it on a test—problem-solving classes demand that the pupils execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy. The point is not to accurately execute algorithms, although there is, of course, a right answer... Truly thinking the problem through—creatively applying what you know about math and puzzling out possible solutions—is more important."

The article concludes by noting that programs like No Child Left Behind have focused on minimal standards, rather than enrichment activities for advanced students. The result is a disparity in economic backgrounds for students in pricey math activities; many middle-class Americans investigate summer camps or sports programs for younger kids, but they don't realize how important a math program could be for a curious child. As Daniel Zaharopol, founder of a related non-profit initiative, noted in his searches to recruit low-income students: "Actually doing math should bring them joy."

An anonymous reader writes: The BBC has now put the second of Stephen Hawking's Reith Lectures up on their web site, with accompanying illustrations. It's not 'All you ever wanted to know about Black Holes', but it's an easy introduction to some of the latest thinking on them.

theodp writes: Teaching kids computer science is a great movement," writes HS senior David Yue, "however, to overly dilute the magnitude of the difficulty in regards to the subject area of coding and to create the illusion of mastering a 'superpower' (Code.org) is a huge mistake. There are many videos and articles on the Internet these days that have demonstrated positive support towards computer science education. Below these articles, one can find many comments, left mostly by parents and supporters. These people usually express how proud they are that their children have an opportunity to learn computer science or how proud they are that computer science is being integrated at a more substantial level into the education system." But Drag and Drop Doesn't = Coding, argues Yue. "Parents and teachers today who aren't technical need to be aware that the drag and drop code or the candy-coated learning process does not effectively teach children programming but eventually causes a huge amount of shock once they are immersed in real code." Yue's Emperor's-New-Code warning comes days before President Obama — a graduate of Code.org's drag-and-drop Disney Princess coding tutorial — asks Congress for $4-billion-and-change in the upcoming budget to fund his "Computer Science for All" K-12 initiative.

An anonymous reader writes: Bitcoin capitalist Mircea Popescu has opened a contest to find a new block cipher and is offering a 10 Bitcoin reward for a winning submission. The eccentric Popescu was previously featured on Slashdot for saving OpenBSD from their electric bill in their time of need.

schwit1 writes: While it was hard to call a winner between Hillary Clinton and Bernie Sanders last night, it's easy to say who was luckier. The race between the Democrat presidential hopefuls was so tight in the Iowa caucus Monday that in at least six precincts, the decision on awarding a county delegate came down to a coin toss. And Clinton won all six, media reports said.

sciencehabit writes: Tracking and recording the motion of the sun, the moon, and the planets as they paraded across the desert sky, ancient Babylonian astronomers used simple arithmetic to predict the positions of celestial bodies. Now, new evidence reveals that these astronomers, working several centuries B.C.E., also employed sophisticated geometric methods that foreshadow the development of calculus. Historians had thought such techniques did not emerge until more than 1400 years later, in 14th century Europe.

An anonymous reader writes: Who doesn't love a good conspiracy theory? Well, I don't — they're usually annoying daydreams from annoying people. Fortunately, an Oxford mathematician seems to feel the same way. Dr. David Grimes just published research in PLOS One establishing a formula for determining the likelihood of a failed conspiracy — in other words, how likely some of its participants are to spill the beans. There are three main factors: number of conspirators, the amount of time passed since it started, and how often we can expect conspiracies to intrinsically fail (a value he derived by studying actual conspiracies that were exposed). From the article: "He then applied his equation to four famous conspiracy theories: The belief that the Moon landing was faked, the belief that climate change is a fraud, the belief that vaccines cause autism, and the belief that pharmaceutical companies have suppressed a cure for cancer. Dr. Grimes's analysis suggests that if these four conspiracies were real, most are very likely to have been revealed as such by now. Specifically, the Moon landing 'hoax' would have been revealed in 3.7 years, the climate change 'fraud' in 3.7 to 26.8 years, the vaccine-autism 'conspiracy' in 3.2 to 34.8 years, and the cancer 'conspiracy' in 3.2 years."

peetm writes: I have an above averagely bright nephew, aged 10, who's into maths and whose birthday is coming up soon. I'd like to get him a suitable present – most likely one that's mathematically centred. At Christmas we sat together while I helped him build a few very simple Python programs that 'animated' some simple but interesting maths, e.g., we built a factorial function, investigated the Collatz conjecture (3n + 1 problem) and talked about, but didn't implement Eratosthenes' Sieve – one step too far for him at the moment perhaps. I've looked about for books that might blend computing + maths, but haven't really found anything appropriate for a 10-year-old. I should be indebted to anyone who might suggest either a suitable maths book, or one that brings in some facet of computing. Or, if not a book, then some other present that might pique his interest.

theodp writes: GeekWire reports that Melinda Gates concluded a Davos panel discussion about gender parity with a personal story about her own family, explaining how she originally became interested in computer science, and how she later played Lab Manager to Bill's Mr. Wizard to help pass along their passion for science and math to their kids. "On Saturday mornings," Gates explained, "I wanted to sleep late. So you know what I did? I made sure there were science projects available, and that's what he did with our two daughters and our son. And guess what my two daughters are interested in? Science and math."

mspohr writes: This article makes a fairly persuasive argument for the utility of the blockchain. It discusses a wide variety of companies and government exploring blockchain to maintain secure records which cannot be altered. One interesting application is to use blockchain to maintain property records in many countries where these records are often incomplete and are easily corrupted (intentionally or unintentionally). A linked article in The Economist expands the thought and discusses changes to the blockchain to improve performance, reduce overhead and accommodate different uses. (See also this related poll.)

Reader John Tromp points to an explanation posted at GitHub of a computational challenge Tromp coordinated that makes a nice companion to the recent discovery of a 22 million-digit Mersenne prime. A distributed effort using pooled computers from two centers at Princeton, and more contributed from the HP Helion cloud, after "many hiccups and a few catastrophes" calculated the number of legal positions in a 19x19 game of Go. Simple as Go board layout is, the permutations allowed by the rules are anything but simple to calculate: "For running an L19 job, a beefy server with 15TB of fast scratch diskspace, 8 to 16 cores, and 192GB of RAM, is recommended. Expect a few months of running time." More: Large numbers have a way of popping up in the game of Go. Few people believe that a tiny 2x2 Go board allows for more than a few hundred games. Yet 2x2 games number not in the hundreds, nor in the thousands, nor even in the millions. They number in the hundreds of billions! 386356909593 to be precise. Things only get crazier as you go up in boardsize. A lower bound of 10^{10^48} on the number of 19x19 games, as proved in our paper, was recently improved to a googolplex. (For anyone who wants to double check his work, Tromp has posted as open source the software used.)

New submitter mtapman writes: I'm looking for suggestions on introductory software engineering projects for a high school level student. Assume the student can do basic math (up through Algebra I or Statistics I) but is new to logic and computer science. Each project should take no more than four hours to complete including research, coding, and testing. The intent is to introduce the student to software engineering (and computer science) through practical and fun examples. Classic CS problems are welcome. One of the key criteria is available research/reference material to allow the student to make progress with 30-60 minutes of online research.

Some ideas that came to my mind (not necessarily good ones) are: (1) pick a sorting algorithm and sort a list of ten words alphabetically, (2) write a program to convert characters from lower to upper case, (3) write a program to divide two numbers in two different programming languages and compare the results to determine the differences between the languages.

theodp writes: Just days after it came under fire for dismissing a call for diversity as "unduly burdensome and not necessary," Apple quietly released its 2015 EEO-1 diversity report (dated 10/6/2015, reflects the 8/1 payroll). Like other tech companies' diversity disclosures, Apple's EEO-1 raw numbers can't really be reconciled to the percentages based on undisclosed raw numbers that grace the infographic-heavy diversity progress narrative CEO Tim Cook spoke to last August. As to why they keep two sets of diversity books, Apple explains, "The EEO-1 has not kept pace with changes in industry or the American workforce over the past half century. We believe the information we report elsewhere on this site is a far more accurate reflection of our progress toward diversity." Taking this stance allows Apple CEO Tim Cook to boast that "in the United States, we hired more than 2,200 Black employees — a 50 percent increase over last year," while ignoring Apple's EEO-1 report, which indicates that Black employees showed a year-over-year net increase of only 1,475 employees and accounted for only 1.9% of the 4,333 YOY net increase in "Professionals" at Apple (White employees accounted for 50.6%, Asian for 42.1%). If you want to check the math, Apple's EEO-1 data (typed in from the content-copy-not-allowed 2015 and 2014 PDFs) and additional charts can be found in this Tableau workbook.

destinyland writes: Tuesday's State of the Union address included a shout-out to Katherine Johnson, the pioneering African American mathematician and physicist who calculated the trajectory of Alan Shepherd's 1961 space trip. "Her reputation was so strong that John Glenn asked her to recheck the calculations made by the new electronic computers before the mission on which he became the first American to orbit the Earth," notes one technology reporter. NASA policy at the time was to not acknowledge the female contributors to scientific papers, though "She literally wrote the textbook on rocket science," according to one NASA official, noting that her impact literally reaches all the way to the moon. At a ceremony in November, Johnson was awarded the Presidential Medal of Freedom, and the 97-year-old pioneer continues to encourage young people to also pursue careers in technology, science, engineering and math.

theodp writes: In A New Chapter for Computer Science Education, the U.S. Department of Education explained earlier this month that the federal STEM Education Act of 2015 'provides an unprecedented opportunity to fully leverage federal resources' to address large gaps in students' participation in Advanced Placement (AP) computer science classes based on gender and race. "In three states," lamented the DOE, "not a single female student took the AP computer science exam" (that only 8 boys took the AP CS exam in those same 3 states was apparently not a concern). And the DOE has good news for those hoping to tap Title I and II funds for CS, but don't have any computer science teachers. "A background in math or science isn't necessarily a requirement to teach CS," explains the Dept. of Ed, "as disciplines like English, history and civics can also provide a solid foundation for teaching CS concepts."

szczys writes: It is surprising to learn how broken the JavaScript Random Number Generator has been for the past six years. The problem is compounded by the fact that Node.js uses the same broken Math.random() module. Learning about why this is broken is interesting, but perhaps even more interesting is how the bad code got there in the first place. It seems that a forum thread from way back in 1999 shared two versions of the code. If you read to the end of the thread you got the working version, if you didn't make it that far (perhaps the case with JavaScript devs) you got the bad version of the code whose fix is just now being rolled out.

dkatana writes: AWS started out defining its virtual CPUs as being composed of EC2 compute units, or ECUs, which it defined as an equivalent to a physical Xeon processor. However, a virtual CPU now looks suspiciously variable... A virtual CPU is whatever Amazon wants to offer in an instance series. The user has no firm measure to go by. From the article: [B]y doing a little math, you could actually compare what you were getting in virtual CPUs in EC2 versus Azure. Also by doing a little math, you knew how to compare one Amazon instance to another based on the ECU count in each virtual CPU. Microsoft didn't look too bad in the comparison. That is one of the casualties of the nomenclature change. I have searched for updated information on how a virtual CPU is measured and found nothing comparable to the definition of the 2012 ECU measure. I have questioned Amazon representatives three times between Oct. 27 and Dec. 21, and don't have much of an answer."