The 100 Top Science Stories of 2010

Every year Discover magazine lists its 100 Top Science Stories, and a number of these stories, particularly those involving physics and engineering, require a lot of math in their execution. Beyond that, however, four of the stories feature mathematics centrally. In numerical order:

  • In #51 A Computer Rosetta Stone we find a computer program that deciphers ancient heiroglyphics statistically. MIT computer scientist Regina Barzilay has developed the program, which compares unknown letters and words to letters and words of known languages in order to find parallels. When she tested it by seeing how much of ancient Ugaritic the program could decipher using the related language Hebrew as the ‘parallel’, the program correctly matched 29 of the 30 Ugaritic letters to their Hebrew equivalent, and 60% of the Ugaratic words that had Hebrew cognates. More importantly, it did the work in a matter of hours, whereas human translators needed decades (and the chance find of an ancient Ugaritic axe that had the word “axe” carved on it) to accomplish similar feats. While the program certainly cannot replace the intuition and feel for language that human scientists possess, “it is a powerful tool that can aid the human decipherment process,” and could already be of use in expanding the number of languages that machine translators can handle.
  • #60 Fighting Crime with Mathematics details the work of UCLA mathematicians Martin Short and Andrea Bertozzi who, along with UCLA anthropologist Jeff Brantingham, developed a mathematical model of the formation and behavior of crime ‘hotspots.’ After calibrating the model with real-world data, it appears that hotspots come in two varieties: “One type forms when an area experiences a large-scale crime increase, such as when a park is overrun by drug dealers. Another develops when a small number of criminals—say, a pair of burglars—go on a localized crime spree.” According to the work, the typical police reaction of targeting the hotspots appears to work much better on the first type of hotspot, but hotspots of the second type usually just relocate to a less-patrolled area. As the story notes, “By analyzing police reports as they come in, Short hopes to determine which type of hot spot is forming so police can handle it more effectively.”
  • There seems to be a steady stream of stories recently that remark on how some animals instinctively know the best way to do things. One example from this blog is Iain Couzin’s work on animal migration. And here’s another: #92 Sharks Use Math to Hunt. Levy flight is the name given a search pattern which has been long suspected by mathematicians of being one of the most effective hunting strategies when food is scarce. David Sims of the Marine Biological Association of 
the United Kingdom logged the movements of 55 marine animals from 14 different species over 5,700 days, and confirmed that the fish movements closely matched Levy flight. (The marine animals included tuna and marlin, by the way, but sharks always get the headlines.)
  • #95 Rubik’s Cube Decoded covers a story already mentioned on this blog about “God’s Number”, the maximum number of moves that an omniscient being would need in order to solve any starting position of Rubik’s cube. The answer, as you can read in this story or by reading my earlier blog post, is 20.

The whole Top 100 is worth going through as well. It’s remarkable to realize how much and how quickly science is learning in this day and age.

The 10th Annual Year in Ideas

NY Times 2010 Year In Ideas

Another year has passed, which means it’s time again for the NY Times Magazine’s annual The Year in Ideas issue, “a high-to-low, silly-to-serious selection of ingenuity and innovation from 2010.” As with the 2009 list, a number of these ideas are based around some bit of mathematics and/or statistical analysis. The ones I’ve listed below are the ones that most prominently feature mathematics ideas, or feature mathematics and/or mathematicians centrally.

  • Perfect Parallel Parking by Jascha Hoffman mentions Simon Blackburn’s geometric analysis of parallel parking, which we covered on the blog previously. Updating that earlier story, Hoffman’s entry notes that Jerome White and some fellow teachers at Lusher Charter School in New Orleans subsequently improved the model. (White and company built in allowances for the driver to do a bit more maneuvering.)
  • Aftercrimes visits a topic seen already here in this blog: just as earthquakes typically beget aftershocks, some types of crime beget copycat crimes. Mathematician George Mohler has been able to show that “the timing and location of the crimes can be statistically predicted with a high degree of accuracy.” For more info, check out the entry and the earlier blog post.
  • The entry Social Media as Social Index describes some of the ways that researchers—academic, government, and corporate—are mining social networks like Twitter and Facebook for valuable information. For instance, algorithms analyzing millions of Twitter posts were able to predict how certain movies would perform at the box office and how the Dow Jones Industrial Average would perform in the near future. More social media data mining is undoubtedly in store, as the story ends with one Facebook officer quoted as saying that this is the future of opinion research.
  • Finally, two entries which illustrate the public appetite for data analysis. Do-It-Yourself Macroeconomics describes the growing legion of “ordinary citizens” who are making it their business to “pull apart the [economic] data and come to their own conclusions.” All this is possible, of course, due to the explosion in publicly available economic data, one example of which is described in The Real-Time Inflation Calculator. As the story concludes, thanks to this (freely available) software, “Data on prices, once monopolized by government gatekeepers, are now up for grabs.”

Popular Science’s Brilliant 10

Each year the magazine Popular Science dubs 10 young scientists their “Brilliant 10”, highlighting the scientists’ work and its implications. In the 2010 edition, more than a few of the profiled rely on mathematics. The work of two, Iain Couzin and Paul Rabadan, are especially mathematical and I’ll mention them here.

Iain Couzin, “the Pattern Maker”, works in ecology and biology, and specializes in identifying the rules that underlie the movements of groups of animals.

The shuffle of life—the wheeling of birds, the silver flash of escaping fish—looks mystically organized. Iain Couzin, who models collective behavior in nature, identifies those patterns mathematically. And he’s finding that certain patterns extend across otherwise unrelated units of life, whether bugs or cancer cells.

This is, of course, one of the great strengths of mathematics: once abstracted, it is easy to recognize a pattern that occurs in different places. Some of Couzin’s earlier work—featured in articles in National Geographic and the NY Times, for instance—involved divining the rules that army ant colonies use to direct their devastating raids. His most recent work, mentioned in Discover, provides an explanation for the large migrations seen in so many animal species. The model, if correct, also provides a warning: tampering with the migrating herds, through hunting or habitat alteration, could devastate the migration instinct itself.

Migration could disappear in a few generations, and take many more to come back, if at all. Indeed, bison in North America no longer seem able to migrate, a fate that may soon be shared by wildebeest in the Serengeti. Migration may vanish at a scale measured in human years, and recover at time scales measured in planetary cycles.

Raul Rabadan, “the Outbreak Sleuth” has a background in string theory, but his numerical experience is serving him well now in his hunt for the agents behind various biological diseases.

Raul Rabadan hunts deadly viruses, but he has no need for biohazard suits. His work does not bring him to far-flung jungles. He’s neither medical doctor nor epidemiologist. He’s a theoretical physicist with expertise in string theory and black holes, and he cracks microbial mysteries in much the same way he once tried to decode the secrets of the universe: He follows the numbers.

Rabadan has been a pioneer of a data analysis technique called Frequency Analysis of Sequence Data that has been able to pinpoint previously unknown viruses as the cause of major disease outbreaks in various animal (and human) populations. Some of his work focused on tracing the origins of the H1N1 swine flu virus, with articles about the work appearing in Wired and online at CNN and USA Today.

A Disappearing Number

A Disappearing Number is a new play by Simon McBurney and London’s Theatre Complicite. As with a number of modern plays and books the storyline actually consists of two separate and non-linear storylines, each one resonating with the other at different moments and in different manners. Unusually for modern plays, however, both stories are centered around mathematics:

McBurney likes to confront difficult subjects in his theater work. Like a lot of people, he’s scared by mathematics — which is why, he says, “I wanted to create a show in which mathematics was absolutely at the center of it.”

One of the storylines concerns the real-life association of the mathematicians G.H. Hardy and Srinivasa Ramanujan in the early 20th century. The second storyline involves a fictional present-day relationship between Ruth, a mathematics professor fascinated by Ramanujan’s work, and Al, an Indian-American hedge fund trader. Throughout, mathematical ideas like infinity, parallels, and even weighty topics like string theory augment the emotional and narrative dimensions of the play’s events.

A Disappearing Number got rave reviews in London, dominating the Olivier awards there. (The Olivier awards are the British equivalent of the Tonies here.) The quote above is from a story on NPR about the play, but any number of almost uniformly positive reviews (for example, from the NY Times, where the image above is taken from) are available online by doing a search on the title.

The Ninth Annual Year in Ideas

2009 Year In Ideas

The NY Times Magazine annually publishes its The Year in Ideas issue, devoted entirely to “the most clever, important, silly and just plain weird innovations … from all corners of the thinking world.” A surprising number of these ideas are based on a study or research article or something similar that employs some bit of mathematical and/or statistical analysis. The ones I’ve listed below are chosen as being the ones that most prominently feature mathematics ideas, or feature mathematics and/or mathematicians centrally. Listed alphabetically:

  • Black Quarterbacks Are Underpaid by Jason Zengerle describes the statistical analysis of two economists, David J. Berri and Rob Simmons, who discovered that in the NFL black quarterbacks are typically paid much less than white quarterbacks. Their analysis goes farther, however, and notes that the apparent cause is not necessarily racism. Instead, the NFL quarterback rating statistic is the culprit. NFL contracts are often based on hitting certain statistical levels, and for quarterbacks the statistic used is often the QB rating. Since QB rating fails to count rushing yards at all–something that black quarterbacks typically excel at–black quarterbacks are typically ‘discounted’, QB rating-wise.
  • Forensic Polling Analysis visits a topic seen already here in this blog: the suspicious polling numbers of the polling firm Strategic Vision LLC. You can visit that entry or the Times article for more info.
  • In a blow to meritocracy-lovers everywhere, another entry notes that Random Promotions, rather than merit-based ones, can actually produce better businesses (and typically do, at least in simulations). The article by Clive Thompson describes a study done by a trio of Italian scientists in which the researchers created a virtual 160-person company and then tried out various different promotion schemes within the company, with the aim of seeing which scheme improved the company’s productivity the most. Promoting on merit turned out to be a lousy idea (at least for the company as a whole) while promoting at random turned out to be the top strategy. In the middle was the curious idea of alternately promoting the best and then the worst employees. The fact that the mixed best/worst strategy outperformed the merit strategy is yet another example of Parrando’s Paradox, a phenomenon first identified by game theory.
  • Massively Collaborative Mathematics features the first mathematical theorem proved by a ‘collective mind’, if you will. In January 2009, Timothy Gowers, one of the top mathematicians in the field, proposed on his blog that the mathematical community, as a whole–or at least that portion that knew and read his blog–attack a long-standing unsolved problem in mathematics known as the Density Hales-Jewett Theorem. Contributors ranged from eminent mathematicians to high school teachers, and hundreds of thousands of words worth of ideas were eventually proposed, developed, discarded, combined, and so forth. Gowers had initially set the bar low, hoping this ‘Polymath’ project would result in “anything that could count as genuine progress toward an understanding of the problem.” Instead, six weeks later the problem was completely solved. A paper detailing the result, authored by D.H.J. Polymath, has been submitted to a leading journal.
  • Finally, the (alphabetically) last idea listed, “Zombie-Attack Science,” features a story that appeared on this blog previously. See that entry, or the Times article, of course, for details.

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.

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.

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.

Best Science Visualization Videos of 2009

Wired magazine presents the best science visualization videos of 2009:

The Department of Energy honored 10 of this year’s best scientific visualizations with its annual SciDAC Vis Night awards, at the Scientific Discovery through Advanced Computing conference (SciDAC) in June. Researchers submitted visualizations to the contest, and program participants voted on the best of the best. From earthquakes to jet flames, this gallery of videos and images show how beautiful (and descriptive) visual data can be.

All of these videos are of course essentially illustrations of mathematical models, models that are so complex that just making the individual frames of the videos requires heavy-duty mathematics and heavy-duty computational power.