Hard Problems

Hard Problems is a documentary about the members of America’s International Math Olympiad (IMO) team. The IMO is an annual competition that pits the top high school math students from various countries against each other, nominally—but in actuality each of them is pitted against an exceptionally challenging mathematics test. (In its 50 years of existence, only once has a team aced the test: the American team of 1994.) The documentary is a great behind-the-scenes peek at the competition, the members, and their experiences.

The documentary will be running on various American Public Television stations across the nation, and a schedule is here. The trailer for the film is here. More information about the DVD and purchasing options can be found here.

Doing the math on Belichick’s decision

When the New England Patriots and Indianapolis Colts met this NFL season it was obvious beforehand that the game would be a good one. Winners of 2 of the past 3 Super Bowls, the teams sported future Hall of Fame quarterbacks and at least one future Hall of Fame coach: Bill Belichick, the most successful NFL coach of the past decade. What was unexpected, perhaps, was that the game would essentially hinge on one play and one decision by Belichick. That decision was to “go for it” on a fourth down play deep in the Patriots own territory rather than punt the ball far down the field, a decision that was virtually unprecedented.

Unprecedented, maybe, but not unadvised. For years statistical analysts have been crunching the numbers on the various league-wide probabilities of success and failure and suggesting that the alternative strategy of never punting is the better one. Despite these conclusions, NFL coaches had–up until Belichick’s decision–continued business as usual and routinely punted when in similar situations. And as expected Belichick was pretty much excoriated by his peers for even contemplating going for it.

Belichick’s decision brought the aforementioned analysis to the fore, and for a few days statistics took center stage on the sports pages. Calculations and debate appeared on ESPN (including at their online site here), as well as at the NY Times, the Boston Globe, and countless blogs and discussion boards. Even the Freakonomics site weighed in.

(And in case you did not know, the Patriots failed on their fourth down try, and ended up losing the game.)

Q&A: Author Malcolm Gladwell


A very short interview, and so a very short note here. But Malcolm Gladwell, the mega-bestselling author of The Tipping Point, Blink, and Outliers, has come down firmly for more math in the media. (Not more of this blog specifically, that is, but actually more math in the media.) Specifically, in this Time magazine interview, he advocates:

Aspiring journalists should stop going to journalism programs and go to some other kind of grad school. If I was studying today, I would go get a master’s in statistics, and maybe do a bunch of accounting courses and then write from that perspective…. Journalism has to get smarter.

Statistics is getting some good press lately. See also the earlier NY Times article “For Today’s Graduate, Just One Word: Statistics.”

The Predictioneer’s Game

We’ve seen Bruce Bueno de Mesquita here on this blog before for his work using game theory to predict political events. Now he’s written a book, The Predictioneer’s Game: Using the Logic of Brazen Self-Interest to See and Shape the Future. The book has garnered pretty good reviews from the in the NY Times and Boston Globe, among others, although most reviews admit to being uneasy with the idea that human behavior could ever be predictable to the degree claimed by the author. Which is understandable, especially since one of Bueno de Mesquita’s bedrock axioms is that those humans are behaving selfishly, or at least `looking out for number one’ with any number two a distant afterthought. (The book’s subtitle: Using the Logic of Brazen Self-Interest to See and Shape the Future.)

Whatever your reaction, Bueno de Mesquita’s approach seems to work: the book documents successful predictions of all sorts of things, from naming the successor to Iran’s Ayatollah Khomeni to foretelling the downfall of Pakistan’s Pervez Musharaff. The author has also been retained on a number of occasions by large corporations to weigh in on their decision-making, and the book sports recommendations from former Nobel laureates, a former CIA director and a former Secretary of State. And Bueno de Mesuita was recently bestowed an even higher honor: he was interviewed on the Daily Show.

Between The Folds


The documentary Between the Folds looks at the art and the science of origami. Our blog has had an entry on the mathematics of origami previously; here is the chance for an extended look. The film debuts on PBS in December 2009. There apparently are also free screenings at various locations around the US. A description from PBS’s website:

Think origami is just paper planes and cranes? Meet a determined group of theoretical scientists and fine artists who have abandoned careers and scoffed at graduate degrees to forge new lives as modern-day paper folders. Together they reinterpret the world in paper, creating a wild mix of sensibilities towards art, science, creativity and meaning.

The film has won numerous accolades at various film festivals; check out the webpage for the production company.

Humanity’s Other Basic Instinct: Math

Everyone knows that human brains are hardwired for certain behaviors like music and language. Add another one to the list: math. Neuroscientists are discovering that “our species seems to have an innate skill for math, a skill that may have been shared by our ancestors going back least 30 million years.” An article from the “Brain” section of Discover magazine, details a number of these discoveries. For example, scientists showed people two sets of dots for a split second, and then asked them to pick out the sum of the two sets of dots. The results?

People do fairly well on these tests, which summons up a weird feeling in them: They know they are right, but they don’t know how they got the answer. Even in toddlers who cannot yet count, these studies reveal, the brain automatically processes numbers.

Darwin Plays Game Theory—and Wins


Game theory is a branch of mathematics that explores how people (or entities made up of people, like organizations) make decisions. This article from Discover magazine shows one of the first instances of game theory being applied to animal behavior. The animals in question are ravens, and in 2002 Sasha Dall, a mathematical ecologist at the University of Exeter in England, used game theory to explain why young ravens scout for carrion by themselves but then recruit other birds to join the feast.

Even more impressively, Dall’s model predicted that ravens would likely employ another strategy, one that had never been observed in ravens: gang foraging, where a large group of birds scavenge together. The article describes what happened when scientists looked to see if Dall was correct:

Behavioral ecologist Jonathan Wright of the Norwegian University of Science and Technology discovered this very behavior in the field. He tracked ravens in North Wales by implanting carcasses with different-colored beads that the birds ingested and later coughed up. Analysis of the beads indicated that ravens in some roosts were searching, eating, and benefiting together, just as Dall anticipated.

Some See Numerical Oddity in Pollster’s Election Surveys

Carl Bialik, the “numbers guy” at the Wall Street Journal, writes here about a polling firm that has come under fire for the results it reported concerning the 2008 presidential election. Strategic Vision LLC, a polling firm based in Georgia, was the only polling firm that declined to release any information regarding where its polling numbers came from to the American Association for Public Opinion Research, the industry’s professional organization. Nate Silver, a statistician who writes a political blog, then examined the numbers that made up Strategic Vision’s polls and found extremely unlikely statistical anomalies. Subsequently, Strategic Vision was censured by the AAPOC and appears to have dropped the polling aspect of its business. Other anomalies have since surfaced in the firm’s polls, including one done for the Oklahoma Council of Public Affairs which claimed to show (among other things) that only 23% of the high schoolers there knew who America’s first president was, and that about 10% of the students had listed the two major political parties as ‘Republican and Communist.’

Scientists set sights on invisibility cloaks

A couple of articles, at the online sites for CNN and FoxNews, feature the work of Graeme Milton, a mathematics professor at the University of Utah. People have long imagined materials (like Harry Potter’s invisibility cloak) that would let light ‘pass through’ or ‘bend around’ any object that was cloaked, thus rendering the object invisible. In fact, that dream seems a long way off. However, Milton’s work shows that an alternative idea–cancelling out light waves coming towards an object, much like noise cancellation devices filter out noise–is entirely possible.

Milton’s results are purely mathematical at this point; as he says, “We just do the math and hope other people do the experiments.” But the research represents a new approach to cloaking, one that has wider applicability than to just light waves. “Results from the study demonstrate that it is conceivable to build cloaking devices that generate waves to create a quiet zone to protect oil rigs against incoming tsunami waves, or to create vibrations to neutralize incoming seismic waves from an earthquake.”

Math Mimics Hard-to-Heal Wounds

This brief article from US News & World Report describes a new mathematical model of ischemic wounds. Ischemic wounds are wounds that do not get as much blood flow as normal wounds, and they affect six and a half million Americans each year. The model, developed by Avner Friedman of Ohio State, includes factors that mimic the actions of healing agents like white blood cells, capillary sprouts, blood-vessel-forming proteins and oxygen concentrations, and is the first to accurately predict healing times for these kind of wounds. The hope is that models like this are “the start of something that could give valuable insight to the wound healing problem in the future.”