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A Different Sort of Equation

Danny Abrams uses math to explain human behavior

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Image of Danny Abrams“I’m trying to find examples where mathematical models have potential to pinpoint the way a system of humans behaves.”

Danny Abrams readily admits it: “My research is all over the place.” Fireflies. Obesity. Language. Religion. All are con­nected, in Abrams’s view, as a series of phenomena that can be explained using similar mathematical tools. Now, back from a four-month research stay in Peru under a Fulbright fellowship and armed with a grant from the James S. McDonnell Foundation, Abrams is using his expertise in synchronization and the physics of social systems to create mathematical models of these phenomena that may ultimately give us a new outlook on human behavior.

Abrams’s interest in applied mathematics was cultivated in graduate school at Cornell, where he began working in the area of coupled oscillators, the study of how oscillators behave in groups. An example can be found in groups of fireflies, where the fireflies’ random blinking can suddenly become synchronized. “If you have a surface covered with fireflies,” he says, “you get certain situations where a portion of those fireflies blink randomly while the rest form a spiral-shaped wave of synchronized blinking. It’s a newly discovered type of pattern formation.”

Abrams, assistant professor of engineering sciences and applied mathematics, created a model of this wave, which has implications beyond insect biology. In people with certain kinds of heart defects, for example, the cardiac cells around the heart don’t expand and contract in time with the heartbeat as normal cells do. Instead, the cells contract randomly or in a spiral wave that rotates around the heart. Abrams’s model could help explain how that works.

Synchronization was also a factor in a problem Abrams tackled in gradu­ate school: the opening and subsequent reengineering of the Millennium Bridge in London. When it first opened in 2000, a crowd of revelers began to cross, and the bridge began to sway from side to side. The contractions forced everyone on the bridge to fall into the same side-to-side steps, like penguins, which amplified the shaking.

“Here we had a model of people acting like oscillators,” Abrams says. “This natural cycle of the bridge swaying connected people and made them adapt their footfalls. I’m trying to find other examples where mathematical models can be somewhat predictive or have potential to pinpoint the way a system of humans behaves.”

Perhaps the social system that most interests Abrams is language: he speaks five of them and says language offers a break from his everyday research. “It’s nice not to do math and physics all the time,” he says.

Now he’s combined his hobby with his research to study the phenom­enon of language death. Of the more than 6,000 languages in the world today, most will die with the people who now speak them. Why are so many languages death-bound? Many people point to increased travel and contact between cultures and a greater ability to communicate across language lines. Abrams’s approach to the subject is through dual-language cultures, where there is generally a minority language and a majority language and where, as a model that Abrams created shows, only one can survive.

“My model treats languages as though they are competing for speakers,” Abrams says. “It shows there is a tipping point where the system goes to one language. It gives some insight into why this is happening all over the world.”

In Peru, Abrams researched competition between two languages he has firsthand knowledge of: Spanish and Quechua, an Incan language primarily spoken in the Andes. Abrams studied Spanish in college and graduate school and learned Quechua after being recruited by a professor who stood outside his Spanish class. About 83 percent of Peruvians speak Spanish as their primary language, and about 13 percent primarily speak Quechua. Abrams asked students at the Universidad Nacional de San Antonio Abad del Cusco which language they spoke, which language their parents spoke, and what por­tion of the people in their hometowns spoke Quechua or Spanish. “I wanted data about how people’s social networks affect their probability of changing languages,” he says.

Though Quechua isn’t in danger of dying anytime soon, it makes a good case for a dual-language model. Studies have shown that two factors drive language change: the majority effect, in which people benefit if they can communicate with more of their peers (and therefore gain an advantage when switching to a majority language), and the status effect, in which soci­ety provides greater benefits to those who speak a language that has a higher status. In Peru and much of South America, Spanish is regarded as an urban, higher-class language, while Quechua is mostly spoken in poorer, rural areas. Abrams hopes to conduct a wider survey that will help him expand his model of language competition to include social networks.

Abrams recently received a three-year grant from the James S. McDonnell Foundation, which funds complex systems research. With this money Abrams hopes to study more systems involving groups competing for members. For example, he is working on a model of competition between religious and nonreligious groups using census records from nine different countries. The 2008 American Religious Identification Survey found that Americans who don’t identify with any particular religious group are the fastest growing religious minority. In the Netherlands, those who affiliate with a religion are now in the minority. Using his language competition model as a basis, Abrams has preliminary results that show how religious affiliation can shift.

Abrams’s research has branched out into other areas of human experi­ence, such as obesity. Obesity rates in the United States stand at 30 percent, and recent studies show that the chance of an individual’s becoming obese strongly correlates with obesity rates of his or her social network. Abrams hopes to create a model that shows how biological and social factors affect the way a person’s weight changes over time.

Abrams is also interested in why about 10 percent of the population is left-handed. Abrams believe it’s an indication of the balance between cooperation and competition in human evolution: If societies were entirely cooperative, everyone would be same-handed. But if competition were more important, one could expect the population to be 50-50. Lefties compose up to 50 percent of top boxers and baseball players, where being left-handed is a key competitive advantage. Abrams hopes to create a model that shows how competition and conformity create the 90-10 ratio.

“As computers and simulation become more widespread in science, it remains important to create understandable mathematical models of the phenomena that interest us,” Abrams said. “By discarding unnecessary elements, these simple models can give us insight into the most important aspects of a problem, sometimes even shedding light on things—like human behavior—that are seemingly outside the domain of math.”

Emily Ayshford