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.

Tying Shoes: Math May Make Case for How We Lace

This is an older story but I couldn’t resist mentioning it here once I’d heard about it: Burkard Polster has determined the best ways to lace a shoe. Now if you’re like me you may have gone through much of your life blind to the endless shoelace arrangements out there. The diagram above provides you (and me) some clue about the 43,200 possibilities there are. (The 43,200 number is for six eyelets on each side; as the number of eyelets goes up the possibilities increase exponentially.) Which arrangements are cooler or more attractive than the others is a matter of taste, but in terms of things quantifiable it’s apparent that some lacings require more shoelace than others, and that some lacings are stronger than others. Thinking in those terms, which shoelace arrangements give you the strongest fit for your buck? Dr. Polster, a mathematician from the University of Monash in Australia, has done the work to figure it out. His findings help confirm why I and so many others have been so ignorant all these years.

The shoe-tying world is dominated by two lacings. The most popular is a simple crisscross, each end of the shoelace pulled through the next eyelet on the opposite flap. The second common way is to pass one end of the lace from the last eyelet across to the top eyelet on the opposite flap and then zigzag the other end in an N pattern through the eyelets….When the eyelets are narrowly spaced and the flaps relatively far apart, the crisscross lacing is strongest. If the eyelets are farther apart, then the zigzagging N pattern provides the tightest tie.

In short, Dr. Polster has demonstrated that sometime in the past the human brain had already “evolutionarily” figured out the optimal ways to lace shoes, and we’ve been largely doing so ever since. The original scientific article detailing the findings appeared in Nature, and the story was then picked up by National Geographic and the NY Times (where the quote above is taken). If you Google Polster and shoelaces, you’ll see that his foot work has garnered Polster mentions on literally hundreds of websites devoted to shoes, and even a mention of sorts in the May 2007 Women’s Health magazine….where they unfortunately decided he was “nutso” for bothering with the calculations. On a more positive note, Polster was inspired to write a short book about his explorations entitled The Shoelace Book: A Mathematical Guide to the Best (And Worst) Ways to Lace Your Shoes, which appears from the online reviews to be a little more appreciated.

Sizing Up Consciousness By Its Bits

This NY Times article details the efforts of Dr. Giulio Tononi to develop a means to measure a person’s level of consciousness as easily as a blood pressure sleeve measures a person’s blood pressure. Dr. Tononi is one of the world’s experts on consciousness, especially that peculiar form of half-consciousness known as sleep. While most people, researchers included, have long thought of consciousness as a kind of synchronization of brain waves, Dr. Tononi noticed that in particular kinds of unconsciousness, like during epileptic seizures, brain waves were even more synchronized than during wakeful periods. It seemed a new paradigm for consciousness was required. And for that paradigm, Dr. Tononi turned to information theory.

While in medical school, Dr. Tononi began to think of consciousness in a different way, as a particularly rich form of information. He took his inspiration from the American engineer Claude Shannon, who built a scientific theory of information in the mid-1900s. Mr. Shannon measured information in a signal by how much uncertainty it reduced. There is very little information in a photodiode that switches on when it detects light, because it reduces only a little uncertainty…. Our neurons are basically fancy photodiodes, producing electric bursts in response to incoming signals. But the conscious experiences they produce contain far more information than in a single diode. In other words, they reduce much more uncertainty.

Tononi has developed a measure called phi that seems to track how rich in information a mental state is, and the article mentions some preliminary medical work that is lending support to his model. The research is in its infancy and much more work is needed, but the same could be said for all science-based inquiries into consciousness. The point here is that the Dr. Tononi’s work “translating the poetry of our conscious experiences into the precise language of mathematics” holds promise—at the very least, enough promise to warrant featuring in this article.


Stephen Colbert coined the word ‘truthiness’ on the very first episode of The Colbert Report, in an attempt to describe statements that have that truthful flavor about them, but without any actual truthful content. The word caught on and entered the lexicon, and the most recent NY Times Magazine On Language column looks back at its five-year history and the “Colbert suffix” that has now come to indicate that ersatz feeling.

Mentioned as an example of the suffix’s spread is Charles Seife’s latest book Proofiness: The Dark Arts of Mathematical Deception. Seife’s book is a look at “the idea that you can use the language of mathematics to convince people something is true even when it is not.” The book is chock full of various people—primarily but not always political people—tinging their speeches, statements, and arguments with ‘mathiness’ in order to make their positions seem to have a factuality and solidity that isn’t really there. The book is getting very good reviews, from the Washington Post, NPR, and the NY Times, for instance. Interviews with Seife can be found here and here, and a brief excerpt appears here.

Artist Leo Villareal

Back in the 1970’s the mathematician John Conway first began exploring cellular automata, a fancy name for patterns that were generated by fairly simple mathematical rules applied over and over and over and over and over…. In Conway’s game, cells on a grid were occupied in whatever initial pattern you liked, and the rules for the next step stated roughly that

  • if too many or too few cells around a space were also occupied (over- or under-crowding), then the cell was emptied or left empty, and
  • if a space was not over- or under-crowded, then it would become or stay occupied.

After Martin Gardner published an article in Scientific American about it the game became known as Conway’s Game of Life. Why that title? Because no matter what initial pattern you started with the patterns that emerged after a few rounds were sometimes eerily life-like. You could swear that you were watching a small society of ants or other small creatures moving around in patterns that you’d expect would require far more sophisticated rules than the actual ones used.

If you Google Conway’s Game of Life you’ll see many, many programs to run it as well as catalogues of patterns that emerge and persist and change, and this idea of “emergent behavior”—simple rules giving rise to sophisticated and nearly-impossible-to-predict patterns—has become an important theme in many parts of science. The artist Leo Villareal has now brought the idea to art. Villareal’s light sculptures are like a souped-up and beautifully tricked out Life. Made up of small LED lights operated by simple rules, Villareal has created art that has been featured in museums and galleries on the East Coast, West Coast, and other places in between. The reviews, of course, don’t really do this kind of art justice, but there are a number of videos (this, this, and this to start) available on YouTube that give some sense of Villareal’s work.

Math Model May Decrease Phantom Traffic Jams

More traffic-related stories here. The ‘phantom’ traffic jams in the title are those where there is no apparent cause. These traffic jams typically occur when there are a lot of cars on the road and some small irregularity—one driver hitting the brakes hard, for instance—starts a chain reaction of driver reactions that blows up back through the line of cars and into a full-fledged stoppage. The “chain reaction” and “blows up” language turns out to be appropriate here. Recently a team of MIT researchers looking at the equations that describe these traffic jams—equations that had been unsolved since the 1950s—made a breakthrough when they realized that the equations were very similar to solved equations describing the detonation of explosives! The story’s combination of cars and explosions was catnip to the media, of course, with the story appearing among other places at MSNBC and Wired and overseas at the Telegraph.

And in another traffic story coming down the pike, another researcher, Morris Flynn at the University of Alberta, has proposed that outfitting cars with some kind of ‘interactive GPS’ could help decrease traffic density and thus decrease the occurrence of these phantom jams. Flynn’s idea was number 39 of Discover’s Top 100 Stories of 2009. Minnesota has used special stoplights at entrance ramps to great effect to do the same thing, as described in Numbers Rule Your World: The Hidden Influence of Probabilities and Statistics on Everything You Do, a recent book by Kaiser Fung.

And finally, to complete this math and traffic pile-up, we have another story featuring Morris Flynn which has an interesting psychological angle. Instead of solving the governing traffic equations, Flynn has been using computers to ‘kick the tires’ of various different mathematical models for traffic flow, and one of the models he investigated looked at those who abide by traffic rules assiduously, the rule-abiders, versus drivers who are willing to bend the rules every now and then, the rule-breakers. Not surprisingly, when rule-breakers rule the road traffic typically doesn’t flow well, since it’s impossible to ‘go with the flow’ if you don’t have a good idea of what the other drivers are going to do. Somewhat surprisingly, rule-abiders don’t do so well by themselves either: when a group of them gets into jams they are in a jam for a good long time. Most surprisingly, traffic works best with a mix of both. In fact, according to Flynn’s calculations a 60%/40% mix of rule-abiders vs. rule-breakers is just about ideal. This story appeared in “A Cure for Traffic Jams: Rule-Breakers” at ABC News.

The Formula for Perfect Parallel Parking

Here’s a problem that may be harder than P vs. NP for some people: parallel parking. Looking for a chance to “show how we can apply mathematics to understanding something that we all share,” mathematician Simon Blackburn of University of London’s Royal Holloway College developed a formula that tells you exactly how much extra length (beyond the length of your car) you need to have to even consider parallel parking in a given space. Blackburn’s formula is fairly comprehensive, taking into consideration the following variables:

r is the radius of my car’s kerb-to-kerb turning circle, l is my car’s wheel-base (the distance between the centres of the front wheel and the corresponding back wheel), k is the distance from the centre of the front wheel to the front of the car, and w is the width of one of the parked cars: the one near the front of my car once I’ve parked.

(As most American readers have probably already guessed, ‘kerb’ is British for ‘curb’.) The story indeed has wide appeal, as the formula has seen mention in places as various as NPR, Fox News, the NY Daily News, and of course outlets in Britain like the Telegraph. Dr. Blackburn’s original paper can be found here.

Step 1: Post Elusive Proof. Step 2: Watch Fireworks.

The P vs. NP problem is a problem about problems. How’s that for problematic? It deals with the class of problems that are solvable by computer and, roughly speaking, it asks whether the class of problems that can be easily solved (that’s P) is the same as the class of problems whose solutions can be easily verified to be actual solutions (that’s NP). It’s suspected that P and NP are very different creatures, if only because everybody wants it to be so: if P = NP then modern cryptography, including things like internet shopping that need it, could theoretically tumble down like a house of cards. These consequences, as well as the problem’s difficulty, are part of what made P vs. NP one of the million-dollar Millennium Prize Problems.

So when Vinay Deolalikar, a researcher at Hewlitt-Packard Labs, thought he had proved that P and NP were indeed distinct, word shot ’round the mathematical community like wildfire. And that is where the story gets interesting in a different way. As happened with recent efforts to prove the Density Hales-Jewett Theorem (see the “Massively Collaborative Mathematics” entry here), an internet community of scholars instantly sprang up and began to go to work, this time on Deolalikar’s paper. Within weeks the proposed proof had been collectively received, reviewed, and dissected by top scholars, a process that in previous generations would have been a logistical nightmare and taken far longer. Unfortunately the proof came up short, although leading researchers credit Deolalikar with coming up with some interesting new ideas. The collective efforts on proving the Density Hales-Jewett Theorem and disproving Deolalikar’s approach have some social scholars believing that the internet could revolutionize research much like the printing press did millennia ago. In effect we may be entering a new research age, one where some major discoveries are “crowd-sourced” and can come at a much faster pace than before. The story was picked up by Nature, the NY Times (whose article provides the title for this post), and the London Telegraph.

Mathematics and Futbol

Soccer has long been one of the team sports with the least amount of statistics, especially statistics on individual players. Unlike (American) football or baseball, say, there are no regular stops in play that break the game into easily digestible chunks; and unlike basketball, say, the ‘important events’ in soccer—like goals, saves, or shots on goal—are relatively rare, and don’t necessarily reveal which team or players are doing well.

Now Luis Amaral and Josh Waitzman from Northwestern University are bridging that gap using, of all things, the mathematics behind social networks. By treating each pass between players as a “link” it is possible to then measure which players are most “central” to the network created and thus, whose presence most helps the team go. Their new metric appears to correlate fairly well with the soccer establishment’s subjective opinions. Is fantasy soccer around the corner? The story was picked up by a number of news outlets, including the Washington Post, Scientific American, and UPI, as well as the online arms of the Discovery Channel and Sports Illustrated. Amaral and Waitzman’s original paper can be found here.

Addendum: A network approach using passing data was also employed by Javier López Peña and Hugo Touchette from Queen Mary University during the 2010 World Cup to analyze teams’ strategies and predict match winners. According to the article “Mathematical Formula Predicts Clear Favorite for the FIFA World Cup” at ScienceDaily, the network predictions’ accuracy rivaled that of the psychic octopus that caught the eye of the news. Dr. Peña was interviewed on CNN Espanol about the mathematical (non-cephalopod) prediction method.