Boing Boing 

Math Fleet: command a space squadron and defend planet Earth with the power of math

Kevin Kelly told me about Phil Scale's new iOS application to teach kids arithmetic. It's called Math Fleet and it sounds great. (Phil created Kevin's Asia Grace photobook app, which is also wonderful.)

Phil says:

I've been an independent iOS app developer for four years, and my wife, Jennifer, and I work together from our home in Austin creating games and educational apps. Our newest app is called Math Fleet, an action game set in space where players must use quick math skills to save Earth from invasion, all while dodging asteroids and battling enemy star fighters.

The inspiration for the game came from our sons, Jack, Luke and Dylan (ages 7, 6 and 3) for whom I've downloaded and tried many educational apps and games. At the beginning of the summer we were all home together and I was brainstorming the next game, which I knew I wanted to set in space. I had my sons Jack and Luke playing a math game I had downloaded to earn playing time for the other games they really wanted to play. We all agreed though that the math game I had them playing, which cost me $5, wasn't a very good game and there really wasn't very much math in it. I knew I could write a better game and we started talking about what we would do differently, and in that moment, we decided our mission was to create not just a better game, but the most awesome action math game out there, and that Jack and Luke would be in the driver's seat guiding how the game would take shape.

It became the ultimate geek dad summer for me as I fully committed myself to making their ideas a reality, and some of their ideas were pretty challenging to implement. Such as Luke's idea that the user pilot multiple ships, customizable and upgradable -- the eventual foundation of the game; Or the Patrol Sector concept drawn up by my 7-year-old, Jack.

Throughout the eight month journey, as I coded, they tested prototypes of controls, menus, action sequences, effects, space weapons, and ships. They told me what they liked and what they didn't like, what they'd do differently, and in many cases they would contribute key design concepts delivered as crayon drawings or Lego models. I learned more about game design by watching them, listening, and discussing ideas than I learned from writing my previous two games.

Finally, after eight months and 300,000 lines of code, Math Fleet is officially released, and is hopefully everything we set out to create to create an exciting math game that kids actually want to play, while also challenging their minds by combining fast problem solving with the stress and distraction of piloting a space fleet.

Math Fleet

Crypto and Bletchley Park podcast from BBC's Infinite Monkey Cage


BBC Radio 4's great math and science show "The Infinite Monkey Cage" did a great (and very funny) episode on crypto and Bletchley Park, with Robin Ince, Brian Cox, Dave Gorman, Simon Singh and Dr Sue Black.

Secret Science

MP3

(via Schneier)

MoMath, more problems

Here's an awesome activity for anybody who happens to be in New York City. Next week, on December 15th, The National Museum of Mathematics (MoMath) will open at a location near the Flatiron Building. Opening weekend festivities (and the museum, itself) look really cool.

Amazing, invisible work that goes on when you click an HTTPS link


Jeff Moser has a clear, fascinating enumeration of all the incredible math stuff that happens between a server and your browser when you click on an HTTPS link and open a secure connection to a remote end. It's one of the most important (and least understood) parts of the technical functioning of the Internet.

People sometimes wonder if math has any relevance to programming. Certificates give a very practical example of applied math. Amazon's certificate tells us that we should use the RSA algorithm to check the signature. RSA was created in the 1970's by MIT professors Ron *R*ivest, Adi *S*hamir, and Len *A*dleman who found a clever way to combine ideas spanning 2000 years of math development to come up with a beautifully simple algorithm:

You pick two huge prime numbers "p" and "q." Multiply them to get "n = p*q." Next, you pick a small public exponent "e" which is the "encryption exponent" and a specially crafted inverse of "e" called "d" as the "decryption exponent." You then make "n" and "e" public and keep "d" as secret as you possibly can and then throw away "p" and "q" (or keep them as secret as "d"). It's really important to remember that "e" and "d" are inverses of each other.

Now, if you have some message, you just need to interpret its bytes as a number "M." If you want to "encrypt" a message to create a "ciphertext", you'd calculate:

C ≡ Me (mod n)

This means that you multiply "M" by itself "e" times. The "mod n" means that we only take the remainder (e.g. "modulus") when dividing by "n." For example, 11 AM + 3 hours ≡ 2 (PM) (mod 12 hours). The recipient knows "d" which allows them to invert the message to recover the original message:

Cd ≡ (Me)d ≡ Me*d ≡ M1 ≡ M (mod n)

The First Few Milliseconds of an HTTPS Connection (via O'Reilly Radar)

Free Coursera Calculus course with hand-drawn animated materials

Robert Ghrist from University of Pennsylvania wrote in to tell us about his new, free Coursera course in single-variable Calculus, which starts on Jan 7. Calculus is one of those amazing, chewy, challenging branches of math, and Ghrist's hand-drawn teaching materials look really engaging.

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include:

the introduction and use of Taylor series and approximations from the beginning;

* a novel synthesis of discrete and continuous forms of Calculus;

* an emphasis on the conceptual over the computational; and

* a clear, entertaining, unified approach.

Calculus: Single Variable (Thanks, Robert!)

Tallest possible Lego tower height calculated


The good folks on the most-excellent BBC Radio/Open University statistical literacy programme More or Less decided to answer a year-old Reddit argument about how many Lego bricks can be vertically stacked before the bottom one collapses.

They got the OU's Dr Ian Johnston to stress-test a 2X2 Lego in a hydraulic testing machine, increasing the pressure to some 4,000 Newtons, at which point the brick basically melted. Based on this, they calculated the maximum weight a 2X2 brick could bear, and thus the maximum height of a Lego tower:

The average maximum force the bricks can stand is 4,240N. That's equivalent to a mass of 432kg (950lbs). If you divide that by the mass of a single brick, which is 1.152g, then you get the grand total of bricks a single piece of Lego could support: 375,000.

So, 375,000 bricks towering 3.5km (2.17 miles) high is what it would take to break a Lego brick.

"That's taller than the highest mountain in Spain. It's significantly higher than Mount Olympus [tallest mountain in Greece], and it's the typical height at which people ski in the Alps," Ian Johnston says.

"So if the Greek gods wanted to build a new temple on Mount Olympus, and Mount Olympus wasn't available, they could just - but no more - do it with Lego bricks. As long as they don't jump up and down too much."

How tall can a Lego tower get?

More or Less: Opinion polling, Kevin Pietersen, and stacking Lego 30 Nov 2012 [MP3]

Some planets are harder to leave than others

At his Psychology Today blog, Michael Chorost delves into a question about exoplanets that I've not really thought much about before — how easy they would be to leave.

Many of the potentially habitable exoplanets that we've found — the ones we call "Earth-like" — are actually a lot bigger than Earth. That fact has an effect — both on how actually habitable those planets would be for us humans and how easily any native civilizations that developed could slip the surly bonds of gravity and make it to outer space.

The good news, says Chorost is that the change in surface gravity wouldn't be as large as you might guess, even for planets much bigger than Earth. The bad news: Even a relatively small increase in surface gravity can mean a big increase in how fast a rocket would have to be going in order to leave the planet. It starts with one equation — SG=M/R^2.

Let’s try it with [exoplanet] HD 40307g, using data from the Habitable Exoplanet Catalog. Mass, 8.2 Earths. Radius, 2.4 times that of Earth. That gets you a surface gravity of 1.42 times Earth.

... it’s amazingly easy to imagine a super-Earth with a comfortable gravity. If a planet had eight Earth masses and 2.83 times the radius, its surface gravity would be exactly 1g. This is the “Fictional Planet” at the bottom of the table. Fictional Planet would be huge by Earth standards, with a circumference of 70,400 miles and an area eight times larger.

Does that mean we could land and take off with exactly the same technology we use here, assuming the atmosphere is similar? Actually, no. Another blogger, who who goes by the moniker SpaceColonizer, pointed out that Fictional Planet has a higher escape velocity than Earth. Put simply, escape velocity is how fast you have to go away from a planet to ensure that gravity can never bring you back. For Earth, escape velocity is about 25,000 miles per hour. Fictional Planet has an escape velocity 68% higher. That’s 42,000 miles per hour.

Read the full story at Psychology Today blogs

Thanks to Apollo 18, who also helped with the math for Chorost's post.

Image: Vintage ad via Christian Montone

Gifts for the space fans in your life

If yesterday's BoingBoing Gift Guide didn't give you enough holiday ideas, Popular Science has a collection of gifts for aspiring rocket scientists. Includes meteorite jewelry, a scarf printed with a pattern inspired by measurement systems, and some natty blazers designed by NASA.

Make a green bean matherole! (And other math-based Thanksgiving treats)

Vi Hart is Khan Academy's professional mathemusician. (Yeah, I KNOW, right?) And, this year, she's making the most delightfully nerdy Thanksgiving dinner ever.

It begins with green bean matherole, topped with fried Borromean onion rings. But, besides the fact that it's finished with crispy, delicious hyperbolic geometry, what makes the matherole a matherole?

Vectors. Like the rings, vectors are part of geometry. They've got a magnitude (think: size of the green bean) and they've got a direction (think: which way the green bean is pointing). Most importantly, a single vector can be part of a field of vectors. And that, my friends, is an excellent starting point for a 9 x 13 pan full of beans.

Klein bottle bottle opener

Yes, it's $72. But this 3-D printed metal sculpture/bottle opener is fantastic. And so is its marketing copy.

The problem of beer That it is within a 'bottle', i.e. a boundaryless compact 2-manifold homeomorphic to the sphere. Since beer bottles are not (usually) pathological or "wild" spheres, but smooth manifolds, they separate 3-space into two non-communicating regions: inside, containing beer, and outside, containing you. This state must not remain.

Read the rest of the product description and, you know, maybe buy the bottle opener, too. If you're feeling spendy.

Via Cliff Pickover

Wall Street is not made up of "numbers guys"

Chad Orzel's post, "Financiers Still Aren’t Rocket Scientists" is a timely reminder that Mitt Romney and other Wall Street Types are not, by and large, superhero math geniuses with their fingers on the arcane numeric truths underpinning all reality. Some quants are genuinely impressive mathematicians, but the industry's reputation for "numbers guys," is just wrong-o.

You would think that the 2008 economic meltdown, in which the financial industry broke the entire world when they were blindsided by the fact that housing prices can go down as well as up, might have cut into the idea of Wall Street bankers as geniuses, but evidently not. The weird idea that the titans of investment banking are the smartest people on the planet continues to persist, even among people who ought to know better– another thing that bugged me about Chris Hayes’s Twilight of the Elites was the way he uncritically accepted the line that Wall Street was the very peak of the meritocracy. It’s not hard to see where it originates– Wall Street types can’t go twenty minutes without telling everybody how smart they are– but it’s hard to see why so many people accept such blatant propaganda without question.

Look, Romney was an investment banker and corporate raider at Bain Capital. This is admittedly vastly more quantitative work than, say, being a journalist, but it doesn’t make him a “numbers guy.” The work that they do relies almost as much on luck and personal connections as it does on math– they’re closer to being professional gamblers than mathematical scientists. This is especially true of Bain and Romney, as was documented earlier this year– Bain made some bad bets before Romney got there, and was deep in the hole, and he got them out in large part by exploiting government connections and a sort of hostage-taking brinksmanship, creating a situation in which their well-deserved bankruptcy would’ve created a nightmare for the people they owed money, which bought them enough time for some other bets to pay off.

Romney has no shortage of nerve, and while he creeps me out, he has the sort of faux charm that works well in the finance community. But he’s not a “numbers guy” in any sense that looks meaningful from over here in the land of science. He can do the math needed to add up his personal fortune, but the game that he made his money playing isn’t a rigorously mathematical one– people get rich in finance as much by playing hunches and cutting sharp deals as by crunching numbers. There are people who make their way in that business by taking a rigorously data-driven approach to investing– one of the many things I need to write up for the blog at some point is a review of a forthcoming book called The Physics of Wall Street– but they’re nowhere near a majority of the industry, and Romney’s not one of them.

Financiers Still Aren’t Rocket Scientists (via Making Light)

Math + Too Much Free Time =

Here is a detailed analysis of the amount of time it would take to ride a hypothetical elevator down through the Earth's core and back out the other side of the planet. Apparently, this has something to do with the remake of Total Recall. But it's interesting even if (like me) you have no intention of seeing that movie. (Via Rhett Allain)

What Nate Silver is actually telling you about the election

The election is next week. And, with that in mind, Salon's Paul Campos has posted a helpful reminder explaining what the statistics at the fivethirtyeight blog actually mean (and what they don't).

In particular, you have to remember that, while Nate Silver gives President Obama a 77.4 percent chance of winning the presidential election, that's not the same thing as saying that Obama is going to win.

Suppose a weather forecasting model predicts that the chance of rain in Chicago tomorrow is 75 percent. How do we determine if the model produces accurate assessments of probabilities? After all, the weather in Chicago tomorrow, just like next week’s presidential election, is a “one-off event,” and after the event the probability that it rained will be either 100 percent or 0 percent. (Indeed, all events that feature any degree of uncertainty are one-off events – or to put it another way, if an event has no unique characteristics it also features no uncertainties).

The answer is, the model’s accuracy can be assessed retrospectively over a statistically significant range of cases, by noting how accurate its probabilistic estimates are. If, for example, this particular weather forecasting model predicted a 75 percent chance of rain on 100 separate days over the previous decade, and it rained on 75 of those days, then we can estimate the model’s accuracy in this regard as 100 percent. This does not mean the model was “wrong” on those days when it didn’t rain, any more than it will mean Silver’s model is “wrong” if Romney were to win next week.

What Silver is predicting, in effect, is that as of today an election between a candidate with Obama’s level of support in the polls and one with Mitt Romney’s level of support in those polls would result in a victory for the former candidate in slightly more than three out of every four such elections.

Read the full story at Salon.com

Fibonacci drawers in a cabinet


Guangzhou's Utopia Design created this Fibonacci Cabinet, whose drawers are scaled according to ratios from the Fibonacci sequence.

Fibonacci Cabint - 乌托邦建筑设计 - UTOPIA ARCHITECTURE & DESIGN: (via Neatorama)

Math journal accepts computer-generated nonsense paper


The peer-reviewed journal Advances in Pure Mathematics was tricked into accepting a nonsense math paper that was generated by a program called Mathgen.

To be fair, the journal did note several flaws in the paper, such as "In this paper, we may find that there are so many mathematical expressions and notations. But the author doesn’t give any introduction for them. I consider that for these new expressions and notations, the author can indicate the factual meanings of them," and requested that they be corrected prior to publication.

However, the "author" of the paper replied with a set of pat rebuttals ("The author believes the proofs given for the referenced propositions are entirely sufficient [they read, respectively, 'This is obvious' and 'This is clear']" and these were seemingly sufficient for the editors.

Sadly, the paper wasn't published, as the "author" wasn't willing to pay the $500 peer-review fee.

On August 3, 2012, a certain Professor Marcie Rathke of the University of Southern North Dakota at Hoople submitted a very interesting article to Advances in Pure Mathematics, one of the many fine journals put out by Scientific Research Publishing. (Your inbox and/or spam trap very likely contains useful information about their publications at this very moment!) This mathematical tour de force was entitled “Independent, Negative, Canonically Turing Arrows of Equations and Problems in Applied Formal PDE”, and I quote here its intriguing abstract:

Let ρ=A. Is it possible to extend isomorphisms? We show that D′ is stochastically orthogonal and trivially affine. In [10], the main result was the construction of p-Cardano, compactly Erdős, Weyl functions. This could shed important light on a conjecture of Conway-d’Alembert.

This is a nice follow-on from the Sokal hoax, wherein a humanities journal was tricked into accepting a nonsense paper on postmodernism. Goes to show that an inability to distinguish nonsense from scholarship exists in both of the two cultures.

Mathgen paper accepted! (via Neatorama)

The music of the primes

Little-scale offers music procedurally-generated from prime numbers. A "full version", available for download, is 26 hours long. [Little-Scale]

Hexaflexagons! The miracle of the inside-out hexagon with many, many sides

The incomparably great Vihart continues her Doodling in Math Class video series with a history and demonstration of the miraculous Hexaflexagon, a simple-to-fold paper hexagon that contains several iterations of itself, which can be found by turning it inside-out over and over again. Sure to delight, inform, entertain, and mystify!

Historical Note: This video is based on a true story. Arthur H. Stone really did invent the hexaflexagon after playing with the paper strips he'd cut off his too-wide British paper, and really did start a flexagon committee (which we'll hear more about in the next video). The details and dialogue, however, are my own invention.

Hexaflexagons (Thanks, Fipi Lele!)

High quality math audio programs from a successful Kickstarter

Peter sez, "Samuel Hansen completed a successful Kickstarter project and as a result has created eight high-quality audio documentaries featuring in-depth stories about the world of mathematics. Samuel describes them: 'While each episode revolves around a single theme, the themes themselves vary widely and include a checkers playing computer, new tools for your mathematical toolbox, and things that were flat out unexpected. The guests range widely too, from a Fields Medalist to a composer to a stand-up mathematician.' Samuel also discusses the benefits of telling stories about mathematics."

I'm in the middle of the game theory episode and loving it!

The Toolbox « Relatively Prime (Thanks, Peter!)

Crazy stuff they'll teach in Louisiana's publicly funded charter schools

Louisiana governor (and retired exorcist) Bobby Jindal has signed an aggressive charter school bill that will transfer millions in tax dollars to religious academies run by evolution-denying, homophobic, climate-change-denying Christian extremists. Mother Jones's Deanna Pan went for a dig through these schools' official texts and discovered that Louisiana's publicly funded education system will soon tell some of its luckiest students that the KKK "achieved a certain respectability" by fighting bootleggers; "the majority of slave holders treated their slaves well;" dragons might be real; "dinosaurs and humans were definitely on the earth at the same time," and many other fun facts.

3. "God used the Trail of Tears to bring many Indians to Christ."—America: Land That I Love, Teacher ed., A Beka Book, 1994...

7. The Great Depression wasn't as bad as the liberals made it sound: "Perhaps the best known work of propaganda to come from the Depression was John Steinbeck's The Grapes of Wrath…Other forms of propaganda included rumors of mortgage foreclosures, mass evictions, and hunger riots and exaggerated statistics representing the number of unemployed and homeless people in America."—United States History: Heritage of Freedom, 2nd ed., A Beka Book, 1996...

10. Mark Twain and Emily Dickinson were a couple of hacks: "[Mark] Twain's outlook was both self-centered and ultimately hopeless…Twain's skepticism was clearly not the honest questioning of a seeker of truth but the deliberate defiance of a confessed rebel."—Elements of Literature for Christian Schools, Bob Jones University, 2001

"Several of [Emily Dickinson's] poems show a presumptuous attitude concerning her eternal destiny and a veiled disrespect for authority in general. Throughout her life she viewed salvation as a gamble, not a certainty. Although she did view the Bible as a source of poetic inspiration, she never accepted it as an inerrant guide to life."—Elements of Literature for Christian Schools, Bob Jones University, 2001...

12. Gay people "have no more claims to special rights than child molesters or rapists."—Teacher's Resource Guide to Current Events for Christian Schools, 1998-1999, Bob Jones University Press, 1998

One text also decries mathematical set theory as ungodly.

14 Wacky "Facts" Kids Will Learn in Louisiana's Voucher Schools

What do Christian fundamentalists have against set theory?

I've mentioned here before that I went to fundamentalist Christian schools from grade 8 through grade 11. I learned high school biology from a Bob Jones University textbook, watched videos of Ken Ham talking about cryptozoology as extra credit assignments, and my mental database of American history probably includes way more information about great revival movements than yours does. In my experience, when the schools I went to followed actual facts, they did a good job in education. Small class sizes, lots of hands-on, lots of writing, and lots of time spent teaching to learn rather than teaching to a standardized test. But when they decided that the facts were ungodly, things went to crazytown pretty damn quick.

All of this is to say that I usually take a fairly blasé attitude towards the "OMG LOOK WHAT THE FUNDIES TEACH KIDS" sort of expose that pops up occasionally on the Internet. It's hard to be shocked by stuff that you long ago forgot isn't general public knowledge. You say A Beka and Bob Jones University Press are still freaked about Communism, take big detours into slavery/KKK apologetics, and claim the Depression was mostly just propaganda? Yeah, they'll do that. Oh, the Life Science textbook says humans and dinosaurs totally hung out and remains weirdly obsessed with bombardier beetles? What else is new?

Well, for me, this is new:

"Unlike the "modern math" theorists, who believe that mathematics is a creation of man and thus arbitrary and relative, A Beka Book teaches that the laws of mathematics are a creation of God and thus absolute....A Beka Book provides attractive, legible, and workable traditional mathematics texts that are not burdened with modern theories such as set theory." — ABeka.com

Wait? What?

Read the rest

When Rudy Rucker met Kurt Gödel


Science fiction writer and mathematician Rudy Rucker -- surely one of the world's all-time happiest mutants -- met with Kurt Gödel on three occasions, which he documented in an essay from his book Infinity and the Mind. Now Rucker has reprinted the essay on his blog, along with some of his fine photographs. It raised goosebumps on my arms.

When I saw him he was dressed as in all his pictures, with a suit over a warm vest and necktie. He is known to have worried a great deal about his health and was always careful to keep himself well bundled-up. Indeed, in the winter, one would sometimes see him leaving the Institute with a scarf wrapped around his head.

He encouraged me to ask questions, and, feeling like Aladdin in the treasure cave, I asked him as many as I could think of. His mind was unbelievably fast and experienced. It seemed that, over the years, he had already thought every possible philosophical problem through to the very end.

Despite his vast knowledge, he still could discuss ideas with the zest and openness of a young man. If I happened to say something particularly stupid or naive, his response was not mockery, but rather an amused astonishment that anyone could think such a thing. It was as if during his years of isolated thought he had forgotten that the rest of the human race was not advancing along with him.

Memories of Kurt Gödel

Should you buy an unlimited-ride Metrocard?

Unless you count a three-month internship in college, I've never lived in New York City. But, between friends and work, I've managed to visit every couple years or so and I've nearly always picked up an unlimited-ride Metrocard for my week in town. Turns out, choosing to do so is an excellent example of Maggie not being super great at math. Michael Moyer has plotted out the numbers on unlimited-ride Metrocards. He says the purchase only makes sense if you're riding a lot—averaging 14 rides a week for the 7-Day-Pass or 12 rides a week for the 30-Day-Pass. Any less and you're actually better off paying a la carte.

How physicist Jim Kakalios invented a math equation for the new Spider-Man movie

Scientific advising for science-fiction films is a really fascinating topic for me. It's a weird, weird world, where the goal is not necessarily extreme accuracy, but extreme believability. That can be a stress point for science, a field that is, generally, all about striving for accuracy. The scientists that help directors create believable worlds have to balance the goal of educating the public with the goal of entertaining same. That can be tough, and it leads some creative solutions—and little educational Easter Eggs buried in the background of blockbusters.

Take the work University of Minnesota physicist Jim Kakalios recently did for the new Spider-Man reboot. The film's creators asked him to invent a complicated-looking equation that, in the context of the story, would relate to cell regeneration and human mortality.

How do you invent a fictional equation? Start with a real one.

In this video, Kakalios explains where his imaginary equation came from, starting with the Gompertz Equation, a very real function that describes mortality rates and can be used to model tumor growth.

Video Link

HOWTO think like Alan Turing

In early celebration of the Turing centenary this week, Ars Technica's Matthew Lasar has a lovely list of seven of Alan Turing's habits of thought, including this one: Be Playful.

There was something about Turing that made his friends and family want to compose rhymes. His proud father openly admitted that he hadn't the vaguest idea what his son's mathematical inquiries were about, but it was all good anyway. "I don't know what the 'ell 'e meant / But that is what 'e said 'e meant," John wrote to Alan, who took delight in reading the couplet to friends.

His fellow students sang songs about him at the dinner table: "The maths brain lies often awake in his bed / Doing logs to ten places and trig in his head."

His gym class colleagues even sang his praises as a linesman: "Turing's fond of the football field / For geometric problems the touch-lines yield."

Turing's favorite physical activity, however, was running, especially the long-distance variety. "He would amaze his colleagues by running to scientific meetings," Hodges writes, "beating the travelers by public transport." He even came close to a shot at the 1948 Olympic Games, a bid cut short by an injury.

The highly productive habits of Alan Turing

(Image: Alan Turing in 1927, Sherborne school archives)

Students assigned to cheat on exam use doctored Little Brother cover and many other clever methods


The IEEE's Computer and Reliability Societies recently published "Embracing the Kobayashi Maru," by James Caroland (US Navy/US Cybercommand) and Greg Conti (West Point) describing an exercise in which they assigned students to cheat on an exam -- either jointly or individually. The goal was to get students thinking about how to secure systems from adversaries who are willing to "cheat" to win. The article describes how the students all completed the exam (they all cheated successfully), which required them to provide the first 100 digits of pi, with only 24h to prepare. The students used many ingenious techniques as cribs, but my heart was warmed to learn that once student printed a false back-cover for my novel Little Brother with pi 1-100 on it (Little Brother is one of the course readings, so many copies of it were already lying around the classroom).

James and Greg have supplied a link to a pre-pub of the paper (the original is paywalled), and sent along a video of a presentation they gave at Shmoocon where they presented the work. The students' solutions are incredibly ingenious -- the audience is practically howling with laughter by the end of the presentation.

(Thanks, Ben!)

Saving dying languages with the help of math

Languages come and go and blend. It's likely been that way forever and the process only accelerates under the influence of mega-languages (like English) that represent a sort of global means of communication. But, increasingly, people who are at risk of losing their native language entirely are fighting back—trying to encourage more people to be bilingual and save the native language from extinction.

At Discover Magazine, Veronique Greenwood has a really interesting story about a mathematician who is helping to preserve Scottish Gaelic. How? The researcher, Anne Kandler, has put together some equations that can help native language supporters target their programs and plan their goals.

Some of the numbers are obvious—you must know how many people in the population you’re working with speak just Gaelic, how many speak just English, and how many are bilingual, as well as the rate of loss of Gaelic speakers. But also in the model are numbers that stand for the prestige of each language—the cultural value people place on speaking it—and numbers that describe a language’s economic value.

Put them all together into a system of equations that describe the growth of the three different groups—English speakers, Gaelic speakers, and bilinguals—and you can calculate what inputs are required for a stable bilingual population to emerge. In 2010, Kandler found that using the most current numbers, a total of 860 English speakers will have to learn Gaelic each year for the number of speakers to stay the same. To her, this sounded like a lot, but the national Gaelic Development Agency was pleased: it’s about the number of bilingual speakers they were already aiming to produce through classes and programs.

Read the rest at Discover Magazine

Image: Gaelic Signs, a Creative Commons Attribution (2.0) image from cradlehall's photostream

How to: Use math to win at Battleship

It takes an average of 66 moves to win a game of Battleship. But that's only if you stick to random guessing. With the help of a computer algorithm, the tech consultant at a data mining company was able to win the game in an average of 44 moves.

Mathematical approximations and how wrong they are

A great XKCD today: "Approximations: A Slightly Wrong Table of Equations and Identities Useful for Approximations and/or Trolling Teachers."

Approximations

Secret Alan Turing cryptanalysis papers released by GCHQ

GCHQ, the UK government's communications headquarters, has published a set of code-breaking papers written by Alan Turing during WWII. The papers had been held in secret since they were written. The papers are c"The Applications of Probability to Crypt" and "Paper on the Statistics of Repetitions" and they deal with cryptanalysis techniques to optimize breaking Nazi ciphers. They're displayed at the National Archives at Kew. The BBC has more:

According to the GCHQ mathematician, who identified himself only as Richard, the papers detailed using "mathematical analysis to try and determine which are the more likely settings so that they can be tried as quickly as possible..."

Richard said that GCHQ had now "squeezed the juice" out of the two papers and was "happy for them to be released into the public domain".

Alan Turing papers on code breaking released by GCHQ (via /.)

Using math to get out of a traffic ticket

We've talked about arXiv here before. It's a pre-print server for scientific papers in the fields of physics, mathematics, and computer sciences. Basically, what that means is that scientists can post papers to the site without first putting that research through the process of peer review. And that's not a bad thing. ArXiv is a great way for scientists and mathematicians to critique each other's work and do a little bit of vetting before submitting the paper to peer review. That's why the faster-than-light neutrino reports were published on arXiv—the results looked so crazy that the researchers wanted their colleagues to figure out what had gone wrong before a prestigious journal got involved. It's a way of collaborating.

The other nice thing about arXiv: It's a great home for interesting data that doesn't necessarily have a place in a formal, peer-reviewed journal.

Case in point: "The Proof of Innocence", a paper in which physicist Dmitri Krioukov uses math to explain why the cop who stopped him for running a stop sign was clearly seeing things. Physics Central summarizes the first step in this defense:

When Krioukov drove toward the stop sign the police officer was approximating Krioukov's angular velocity instead of his linear velocity. This happens when we try to estimate the speed of a passing object, and the effect is more pronounced for faster objects.

Trains, for instance, appear to be moving very slowly when they are far away, but they speed past when they finally reach us. Despite these two different observations at different distances, the train maintains a roughly constant velocity throughout its trip.

In Krioukov's case, the police cruiser was situated about 100 feet away from a perpendicular intersection with a stop sign. Consequently, a car approaching the intersection with constant linear velocity will rapidly increase in angular velocity from the police officer's perspective.

Krioukov's basic argument: The officer thought he saw Krioukov speed right through the sign. But he was wrong. Instead, Krioukov stopped at the sign, but stopped very quickly and sped up quickly, both of which happened out of the cop's direct line of sight.

It's worth noting that this argument was good enough to get Krioukov out of a $400 fine.

Read Krioukov's paper.

Read the summary on Physics Central.

Image: Stop, a Creative Commons Attribution (2.0) image from misteraitch's photostream