For Decades, Puzzling People With Mathematics

For those who don’t know him, Martin Gardner is a unique figure in mathematics: although he never took a math course beyond high school, Gardner “more or less single-handedly renewed and nurtured interest in recreational mathematics in North America for a large part of the 20th century.” (That quote is from his Wikipedia entry.) Among other things, Gardner wrote the ‘Mathematical Games’ column in Scientific American for decades and is the author of over 70 books, many (though not all) of which are devoted to fun and thoughtful mathematical puzzles, and is the centerpiece of the Gathering for Gardner (G4G) conference, held in Atlanta every two years, which attracts a wide variety of mathematicians and puzzlists. For a necessarily tiny selection of number tricks, science fiction puzzles, or columns from Scientific American, just click on the links, or buy the books referenced there.

The NY Times article mentioned in the title commemorates Gardner’s 95th birthday, which also happens to coincide with the release of his latest book. Happy birthday, Martin!

Addendum: Unfortunately Martin Gardner died this past May. In his honor obituaries appeared in all the major newspapers and in many magazines as well. In particular, Scientific American (the magazine for which he wrote for 25 years) re-published a profile of his life from 1995. Good night and God bless, Mr. Gardner.

Fold Everything

Appearing in National Geographic‘s “Big Idea” section, this article details some cool and surprising modern uses of the ancient art of origami, or paper folding. Mathematicians have recently been studying origami using geometric ideas and, as physicist Robert G. Lang is quoted, “It’s now mathematically proven that you can pretty much fold anything.” Some of the designs include folding mirrors and lenses for satellite use, arterial stents for medical use, and at least one common everyday use:

When engineers working on the design of car air bags asked Lang to figure out the best way to fold one into a dashboard, he saw that his algorithm for paper insects would do the trick. “It was an unexpected solution,” he says.

Plugging Holes in the Science of Forensics

This NY Times article discusses the recent National Academy of Sciences (NAS) report that found “serious problems” with many of the forensic ‘sciences’ practiced in crime labs today. Most of these problems are of the mathematical variety: with the exception of DNA evidence, much of the type of research done on the forensic sciences is geared towards finding information at the crime scene, and not geared towards statistically checking how valid and reliable these finds really are in identifying the perpetrator. A foretaste of this came a few years back, when the forensic science of bullet lead analysis (first used to convict Lee Harvey Oswald of the murder of John F. Kennedy) was abandoned by the FBI after an NAS report found it lacking as well.

The article goes on to describe the efforts of various scientists to “refine [the] mathematical tools” being used to put the other forensic sciences on the same level as DNA.

New Music Software Predicts The Hits

NPR’s Morning Edition takes a look at Hit Song Science, a new software program that purports to predict whether a pop song will be a hit or not–and seems to do a fairly good job of it. A study by the Harvard Business School found that the algorithms worked 8 out of 10 times. A sample quote from the Morning Edition broadcast:

Many of us like to believe that there’s a little magic behind the making of a hit single. Take a song like “I Gotta Feeling” by The Black Eyed Peas. That’s a good song, judging by sales: It’s on top of the Billboard pop chart. David Meredith, CEO of Music Intelligence Solutions, says there’s no magic in that; it’s math. His software, called Hit Song Science, gave the song a hit score of 8.9 out 10.

The transcript of the piece is here; the page also contains a link to the audio of the piece itself.

And the Oscar Goes to…Not Its Voting System

When an Oscar winner starts with their “I’d like to thank the Academy…” speech, one of the things they should thank the academy for is the particular way it counts votes. An Oscar voter votes by ranking their top 5 in each Oscar category (with any remaining candidates ignored). The Academy then has to decide what to do with these lists in order to generate a winner. The Oscar for each category is determined using an ‘instant runoff’ system, which is described in this article by Carl Bialik in the Wall Street Journal. The system is not that familiar, although the article notes it’s used in some municipal and state elections as well. Other vote tabulation systems could quite possibly result in different winners. Those systems are described too, as well as the difficulties that they, in turn, present.

Addendum: The vagaries of the instant runoff, and the related plurality systems in voting, were also discussed on Minnesota Public Radio here.

Word Association Mystery Revisited

This article (Spanish-language) in La Nacion describes work whose roots lie in an old project of Sigmund Freud and Carl Jung, among others. Both of those luminaries spent considerable time and effort on the ‘word association problem’: trying to divine when and why certain words were associated with each other in many people’s minds. Mariano Sigman, Martin Elias and Flavia Bonomo of the University of Buenos Aires applied mathematics to the problem, using a huge corpus of text from newspapers and books to develop a metric which determines how “close” and “far” different words typically are from each other. The associations given by their metric appear to do a pretty good job mirroring the responses people give when given a word and asked to say what pops into their head.

2009 MacArthur Fellows Announced

The John D. and Catherine T. MacArthur Foundation annually hands out no-strings-attached “genius grants” of $500,000 each to 24 individuals. As always, this year’s awards are being reported everywhere (AP, UPI, NY Times, USA Today, etc.). The Foundation’s own list of the recipients is here.

Of relevance to this blog, 4 of the 24 recipients are explicitly cited for work that involves mathematics and/or mathematical analysis of data:

  • Esther Duflo, economist.
  • Peter Huybers, climate scientist.
  • L. Mahadevan, applied mathematician.
  • Beth Shapiro, evolutionary biologist.

It’s likely that a few of the other 24 recipients also use mathematics in their work (Maneesh Agrawala, computer vision technologist; John A. Rogers, applied physicist; and Theodore Zolli, bridge engineer, come to mind), but it’s not explicitly mentioned in any of their brief bios.

Shortly after the winners were announced, NPR interviewed Mahadevan about his work and the award.

A $1 Million Research Bargain for Netflix, and Maybe a Model for Others

Netflix is a company that (for a monthly fee) allows you to check out and return movies through the mail. A large number of their customers request movies based on Netflix’s “Cinematch” suggestions, which recommends other movies the customer might like based on the movies he or she has previously ordered. In October 2006, Netflix offered a $1,000,000 prize to anybody who could improve the company’s recommendation algorithm by 10% or more. It proved to be an very difficult and interesting contest, with various mathematical (and other) twists and turns along the way, some of which are sketched here. The prize was recently claimed by a seven-person team of statisticians, machine-learning experts and computer engineers from the United States, Austria, Canada and Israel.

Amazingly, the winning team’s algorithm was mathematically identical to another team’s algorithm, which was submitted only 20 minutes after the winning team’s entry. Still, the second place team is not crying about it:

Yet the scientists and engineers on the second-place team, and the employers who gave many of them the time and freedom to compete in the contest, were hardly despairing. Arnab Gupta, chief executive of Opera Solutions, a consulting company that specializes in data analytics, based in New York, took a small group of his leading researchers off other work for two years. “We’ve already had a $10 million payoff internally from what we’ve learned,” Mr. Gupta said….”So for us, the $1 million prize was secondary, almost trivial.”

The article from which that second quote is taken notes that this type of corporate-led open competition could become a new model for improving business, and mentions a number of other such competitions that have cropped up.

Medieval Mosques Illuminated by Math

This segment from National Public Radio examines the intricate geometric designs that often cover historic buildings in the Islamic world. When Peter Lu, a graduate student at Harvard University, first saw one of them he was reminded of ‘quasicrystal’ patterns he’d encountered in his classes. While it’s doubtful that the creators of the ancient designs knew anything about quasicrystals, it’s equally surprising that their designs–created over 500 years ago–echo these structures that were only identified fairly recently.

For a nice picture of a quasicrystal in another context, also see What Is This? A Psychedelic Place Mat? from Discover magazine here.

Untangling the Mystery of the Inca

The ancient Andean empire built great cities but left no written records – except perhaps in mysterious knotted strings called khipu. Can an anthropologist and some mathematicians crack the code?

That’s the lead-in to this Wired magazine article by Gareth Cook, which details how Harvard anthropologist Gary Urton has turned the pattern-detecting power of mathematics to help decipher khipu, ancient patterns of knots and string that appear to encode information, perhaps even stories or poems, of the Incan empire.