We've mentioned several times over the years the Antikythera Mechanism, the astounding early analog computer recovered from a Greek shipwreck in shape good enough to allow modern recreations. The device has been attributed to different Greek mathemeticians and thinkers, such as Archimedes, Hipparchus, and Posidonius, but as reader puddingebola writes, "Current research suggests its origin may be much earlier, and its working based on Babylonian arithmetical methods rather than Greek Trigonometry, which did not exist at the time. Puddingebola excerpts from the NYT article: Writing this month in the journal Archive for History of Exact Sciences, Dr. Carman and Dr. Evans took a different tack. Starting with the ways the device's eclipse patterns fit Babylonian eclipse records, the two scientists used a process of elimination to reach a conclusion that the "epoch date," or starting point, of the Antikythera Mechanism's calendar was 50 years to a century earlier than had been generally believed.

HughPickens.com writes Gerrymandering is the practice of establishing a political advantage for a particular party by manipulating district boundaries to concentrate all your opponents' votes in a few districts while keeping your party's supporters as a majority in the remaining districts. For example, in North Carolina in 2012 Republicans ended up winning nine out of 13 congressional seats even though more North Carolinians voted for Democrats than Republicans statewide. Now Jessica Jones reports that researchers at Duke are studying the mathematical explanation for the discrepancy. Mathematicians Jonathan Mattingly and Christy Vaughn created a series of district maps using the same vote totals from 2012, but with different borders. Their work was governed by two principles of redistricting: a federal rule requires each district have roughly the same population and a state rule requires congressional districts to be compact. Using those principles as a guide, they created a mathematical algorithm to randomly redraw the boundaries of the state's 13 congressional districts. "We just used the actual vote counts from 2012 and just retabulated them under the different districtings," says Vaughn. "If someone voted for a particular candidate in the 2012 election and one of our redrawn maps assigned where they live to a new congressional district, we assumed that they would still vote for the same political party."

The results were startling. After re-running the election 100 times with a randomly drawn nonpartisan map each time, the average simulated election result was 7 or 8 U.S. House seats for the Democrats and 5 or 6 for Republicans. The maximum number of Republican seats that emerged from any of the simulations was eight. The actual outcome of the election — four Democratic representatives and nine Republicans – did not occur in any of the simulations. "If we really want our elections to reflect the will of the people, then I think we have to put in safeguards to protect our democracy so redistrictings don't end up so biased that they essentially fix the elections before they get started," says Mattingly. But North Carolina State Senator Bob Rucho is unimpressed. "I'm saying these maps aren't gerrymandered," says Rucho. "It was a matter of what the candidates actually was able to tell the voters and if the voters agreed with them. Why would you call that uncompetitive?"

An anonymous reader writes Last week, Riecoin – a project that doubles as decentralized virtual currency and a distributed computing system — quietly broke the record for the largest prime number sextuplet. This happened on November 17, 2014 at 19:50 GMT and the calculation took only 70 minutes using the massive distributed computing power of its network. This week the feat was outdone and the project beat its own record on November 24, 2014 at 20:28 GMT achieving numbers 654 digits long, 21 more than its previous record.

A few days ago you had a chance to ask the people at Hampton Creek about about their products and the science of food. Below you'll find the answers to your questions from a number of Hampton Creek employees.

HughPickens.com writes: Every year the works of thousands of authors enter the public domain, but only a small percentage of these end up being widely available. So how do organizations such as Project Gutenberg choose which works to focus on? Allen Riddell has developed an algorithm that automatically generates an independent ranking of notable authors for any given year. It is then a simple task to pick the works to focus on or to spot notable omissions from the past. Riddell's approach is to look at what kind of public domain content the world has focused on in the past and then use this as a guide to find content that people are likely to focus on in the future.

Riddell's algorithm begins with the Wikipedia entries of all authors in the English language edition (PDF)—more than a million of them. His algorithm extracts information such as the article length, article age, estimated views per day, time elapsed since last revision, and so on. This produces a "public domain ranking" of all the authors that appear on Wikipedia. For example, the author Virginia Woolf has a ranking of 1,081 out of 1,011,304 while the Italian painter Giuseppe Amisani, who died in the same year as Woolf, has a ranking of 580,363. So Riddell's new ranking clearly suggests that organizations like Project Gutenberg should focus more on digitizing Woolf's work than Amisani's. Of the individuals who died in 1965 and whose work will enter the public domain next January in many parts of the world, the new algorithm picks out TS Eliot as the most highly ranked individual. Others highly ranked include Somerset Maugham, Winston Churchill, and Malcolm X.

Bennett Haselton writes: My last article garnered some objections from readers saying that the sample sizes were too small to draw meaningful conclusions. (36 out of 47 survey-takers, or 77%, said that a picture of a black woman breast-feeding was inappropriate; while in a different group, 38 out of 54 survey-takers, or 70%, said that a picture of a white woman breast-feeding was inappropriate in the same context.) My conclusion was that, even on the basis of a relatively small sample, the evidence was strongly against a "huge" gap in the rates at which the surveyed population would consider the two pictures to be inappropriate. I stand by that, but it's worth presenting the math to support that conclusion, because I think the surveys are valuable tools when you understand what you can and cannot demonstrate with a small sample. (Basically, a small sample can present only weak evidence as to what the population average is, but you can confidently demonstrate what it is not.) Keep reading to see what Bennett has to say.

rossgneumann writes Soon, it's very possible that when you say something like "you have better odds of being struck by lightning," that won't necessarily mean it's all that rare. And there's a good chance that you'll be able to tell that person (roughly) what the odds of that happening are. Research published this week in Nature provides an equation that is reasonably accurate at mathematically predicting lightning strikes. From the article: "There's not a whole lot of noise in Romps's estimates: CAPE [Convective Available Potential Energy] is something that can be predicted out fairly easily: "All [models] in our ensemble predict that [the United State's] mean CAPE will increase over the 21st century, with a mean increase of 11.2 percent per degree Celsius of global warming," he wrote. "Overall, the [models] predict a ~50 percent increase in the rate of lightning strikes in the United States over the 21st century."

An anonymous reader writes Alexander Grothendieck, one of the great eccentric geniuses of 20th century mathematics, has died in France at the age of 86. Grothendieck was the leading mind behind algebraic geometry. He was awarded the Fields Medal in 1966. He reached the very pinnacle of his profession before abandoning the discipline, taking up anti-war activism, retreating into the life of a recluse and refusing to share his research. He died on Thursday in a hospital in Saint-Girons in southwestern France.

Bennett Haselton writes: A editorial with 24,000 Facebook shares highlights the differences in public reaction to two nearly identical breastfeeding photos, one showing a black woman and one showing a white woman, each breastfeeding an infant. The editorial decries the outrage provoked by the black woman's photo compared to the mild reaction elicited by the white woman's photo, and attributes the difference to racism. I tried an experiment using Amazon's Mechanical Turk to test that theory. Read on to see the kind of results Bennett found.

rossgneumann writes If everyone always wants to look different than everybody else, everybody starts looking the same. At least, if you use a recently published mathematical model describing the phenomenon. "The hipster effect is this non-concerted emergent collective phenomenon of looking alike trying to look different," in the words of Jonathan Touboul, mathematical neuroscientist at the College de France in Paris.

TaleSlinger writes: One of the great theories of modern cosmology is that the universe began in a "Big Bang", but the mathematical mechanism by which this occurred has been lacking. Cosmologists at the Wuhan Institute have published a proof that the Big Bang could indeed have occurred spontaneously because of quantum fluctuations. "The new proof is based on a special set of solutions to a mathematical entity known as the Wheeler-DeWitt equation. In the first half of the 20th century, cosmologists struggled to combine the two pillars of modern physics— quantum mechanics and general relativity—in a way that reasonably described the universe. As far as they could tell, these theories were entirely at odds with each other.

At the heart of their thinking is Heisenberg's uncertainty principle. This allows a small empty space to come into existence probabilistically due to fluctuations in what physicists call the metastable false vacuum. When this happens, there are two possibilities. If this bubble of space does not expand rapidly, it disappears again almost instantly. But if the bubble can expand to a large enough size, then a universe is created in a way that is irreversible. The question is: does the Wheeler-DeWitt equation allow this? "We prove that once a small true vacuum bubble is created, it has the chance to expand exponentially," say the researchers.

An anonymous reader writes Carnegie Mellon researchers have just launched Spliddit, a website that offers methods for helping people split rent, divide goods, and share credit. The novelty is that these methods are all "provably fair": there are mathematical proofs showing that each algorithm on the site provides rigorous fairness guarantees. For example, the method for splitting rent is guaranteed to be envy free: the assignment of rooms and division of rent is such that a housemate would never want to swap places with another housemate. All it takes is a pair of siblings to prove that there's no such thing as "provably fair," non-mathematically.

An anonymous reader writes: Carol Dweck, a psychology professor at Stanford, has done years of study on how students' attitudes affect their academic achievements. Her work began at the height of the "self-esteem movement," when parents were told to praise their kids' brainpower at every turn. But Professor Dweck found that praise for intelligence or talent — relatively immutable characteristics — only turned kids off of trying subjects they perceived as difficult, like math and science. Praising effort, perseverance, and problem-solving strategies works better. She also says, "There is such a thing as too much praise, we believe." Instead, she suggests engaging with kids about the process itself, showing interest and encouragement when they talk about how they did something.

sciencehabit writes: If you want to figure out how many people live in a particular part of your country, you could spend years conducting home visits and mailing out questionnaires. But a new study describes a quicker way. Scientists have figured out how to map populations using cellphone records — an approach that doesn't just reveal who lives where, but also where they go every day. The researchers also compared their results to population density data gathered through remote sensing technologies, a widely-used method that relies on satellite imaging to gather detailed information on population settlement patterns and estimate population counts. They found that the two methods are comparable in accuracy when checked against actual survey-based census data, but estimates from mobile phone data can provide more timely information, down to the hours.

HughPickens.com writes Clifford Davis reports that only 30% of young people between the ages of 17 and 24 are qualified to become soldiers. This is primarily due to three issues: obesity or health problems; lack of a high school education; and criminal histories. While cognitive and moral disqualifications have held steady, weight issues account for 18% of disqualifications, and the number is rising steadily. It's projected to hit 25% by 2025. The current Army policy is that every recruit, whether enlisting for infantry or graphic design, has to meet the same physical requirements to join — but that requirement may be changing. "Today, we need cyber warriors, so we're starting to recruit for Army Cyber," says Major General Allen Batschelet. "One of the things we're considering is that your [mission] as a cyber warrior is different. Maybe you're not the Ranger who can do 100 pushups, 100 sit-ups and run the 2-mile inside of 10 minutes, but you can crack a data system of an enemy." "We're looking for America's best and brightest just like any Fortune 500 company out there," says Lt. Col. Sharlene Pigg. "We're looking for those men and women who excel in science, technology, engineering and math." Batschelet admits that a drastic change in physical requirements for recruits may be hard for some to swallow. "That's going to be an institutional, cultural change for us to be able to get our heads around that is kind of a different definition of quality," says Batschelet. "I would say it's a modernizing, or defining in a more precise way, what is considered quality for soldiers."

An anonymous reader writes: The Hungarian government has announced a new tax on internet traffic: 150 HUF ($0.62 USD) per gigabyte. In Hungary, a monthly internet subscription costs around 4,000-10,000 HUF ($17-$41), so it could really put a constraint on different service providers, especially for streaming media. This kind of tax could set back the country's technological development by some 20 years — to the pre-internet age. As a side note, the Hungarian government's budget is running at a serious deficit. The internet tax is officially expected to bring in about 20 billion HUF in income, though a quick look at the BIX (Budapest Internet Exchange) and a bit of math suggests a better estimate of the income would probably be an order of magnitude higher.

Any gathering of 65,000 people in the desert is going to require some major infrastructure to maintain health and sanity. At Burning Man, some of that infrastructure is devoted to a supply chain for ice. Writes Bennett Haselton, The lines for ice bags at Burning Man could be cut from an hour long at peak times, to about five minutes, by making one small... Well, read the description below of how they do things now, and see if the same suggested change occurs to you. I'm curious whether it's the kind of idea that is more obvious to students of computer science who think algorithmically, or if it's something that could occur to anyone. Read on for the rest; Bennett's idea for better triage may bring to mind a lot of other queuing situations and ways that time spent waiting in line could be more efficiently employed.

HughPickens.com writes Jim Edwards writes at Business Insider that Google is so large and has such a massive need for talent that if you have the right skills, Google is really enthusiastic to hear from you — especially if you know how to use MatLab, a fourth-generation programming language that allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, Fortran and Python. The key is that data is produced visually or graphically, rather than in a spreadsheet. According to Jonathan Rosenberg , Google's former senior vice president for product management, being a master of statistics is probably your best way into Google right now and if you want to work at Google, make sure you can use MatLab. Big data — how to create it, manipulate it, and put it to good use — is one of those areas in which Google is really enthusiastic about. The sexy job in the next ten years will be statisticians. When every business has free and ubiquitous data, the ability to understand it and extract value from it becomes the complimentary scarce factor. It leads to intelligence, and the intelligent business is the successful business, regardless of its size. Rosenberg says that "my quote about statistics that I didn't use but often do is, 'Data is the sword of the 21st century, those who wield it the samurai.'"

HughPickens.com writes Randy Olson, a Computer Science grad student who works with data visualizations, writes about seven of the biggest factors that predict what makes for a long term stable marriage in America. Olson took the results of a study that polled thousands of recently married and divorced Americans and and asked them dozens of questions about their marriage (PDF): How long they were dating, how long they were engaged, etc. After running this data through a multivariate model, the authors were able to calculate the factors that best predicted whether a marriage would end in divorce. "What struck me about this study is that it basically laid out what makes for a stable marriage in the US," writes Olson. Here are some of the biggest factors:

How long you were dating: (Couples who dated 1-2 years before their engagement were 20% less likely to end up divorced than couples who dated less than a year before getting engaged. Couples who dated 3 years or more are 39% less likely to get divorced.); How much money you make: (The more money you and your partner make, the less likely you are to ultimately file for divorce. Couples who earn $125K per year are 51% less likely to divorce than couples making 0 — 25k); How often you go to church: (Couples who never go to church are 2x more likely to divorce than regular churchgoers.); Your attitude toward your partner: (Men are 1.5x more likely to end up divorced when they care more about their partner's looks, and women are 1.6x more likely to end up divorced when they care more about their partner's wealth.); How many people attended the wedding: ("Crazy enough, your wedding ceremony has a huge impact on the long-term stability of your marriage. Perhaps the biggest factor is how many people attend your wedding: Couples who elope are 12.5x more likely to end up divorced than couples who get married at a wedding with 200+ people."); How much you spent on the wedding: (The more you spend on your wedding, the more likely you'll end up divorced.); Whether you had a honeymoon: (Couples who had a honeymoon are 41% less likely to divorce than those who had no honeymoon)

Of course correlation is not causation. For example, expensive weddings may simply attract the kind of immature and narcissistic people who are less likely to sustain a successful marriage and such people might end up getting divorced even if they married cheaply. But "the particularly scary part here is that the average cost of a wedding in the U.S. is well over $30,000," says Olson, "which doesn't bode well for the future of American marriages."

rastos1 writes: In a recent blog, software developer Bruce Dawson pointed out some issues with the way the FSIN instruction is described in the "Intel® 64 and IA-32 Architectures Software Developer's Manual," noting that the result of FSIN can be very inaccurate in some cases, if compared to the exact mathematical value of the sine function.

Dawson says, "I was shocked when I discovered this. Both the fsin instruction and Intel's documentation are hugely inaccurate, and the inaccurate documentation has led to poor decisions being made. ... Intel has known for years that these instructions are not as accurate as promised. They are now making updates to their documentation. Updating the instruction is not a realistic option."

Intel processors have had a problem with math in the past, too.