Physics Can Solve Child-Custody Arrangements

A mathematical model normally used on "spin-glass systems" can optimize your weekends with the kids
child custody diagram using physics

In this diagram of a child-custody network, female 1 (white circle) has kids with two men. One is married (grey circle 2) and has kids with three women, and the other is single and has children with four women.
Andrés Gomberoff et al.

Physicists usually have full lives outside the lab, despite stereotypes to the contrary (think: the antisocial geniuses on TV's The Big Bang Theory). But when those lives get complicated, they can fall back on their own training to help them out
Case in point is physicist Andrés Gomberoff, who turned to condensed-matter physics to grapple with custodial arrangements for kids with two ex-wives and his current girlfriend. In aiming to find a weekend in which he and his partner could see all their children at once, he applied the same process used to minimize the energy of a certain kind of magnetic material.
Custodial arrangements often allow each parent to spend every other weekend with their kids. Gomberoff wanted a way to see both of his kids as well as his girlfriend's kids on the same weekends, and have every other weekend alone with his girlfriend. "It's important to me to have my two kids together because I want them to grow some brotherhood," he says. "But then I also want to have the kid of my girlfriend on the same weekend so we can have all the kids together. As you can imagine, that can be a difficult problem."
Gomberoff, who usually studies black hole physics at Andrés Bello University in Santiago, Chile, recruited friends from mathematics and complex systems to tackle the problem. The group published their findings in the European Physical Journal B (pdf).
The researchers analyzed a vast network of parents, each with exes who have exes of their own. They wondered if there was an optimal solution that would make every couple happy by seeing all of their kids on the same weekends. "The answer, unfortunately, is no," Gomberoff says. The scientists were able to optimize the network, however, to minimize the number of unhappy couples; they found an algorithm that at least gave every parent all of their own kids on the same weekends (if not their partners’ kids, too).
The custody solution used the same mathematical model developed to find the lowest-energy state of a so-called spin-glass system. This material is made of many tiny magnets, each with its own spin, arrayed together. Because of the magnets' long-range interactions with one another, complex calculations are necessary to find the arrangement that would give the lowest possible energy state. "It was completely crazy that the system was equivalent to a magnetic spin-glass system," Gomberoff says.
Using spin-glass mathematics to model custody arrangements is "a beautiful piece of science," says Vittorio Loreto, a physicist at Sapienza University of Rome who was not involved in the project. "It is neat, mathematically very clean and elegant. Perhaps more
importantly, it takes a social problem, that of the happiness of divorced people, and beautifully formalizes it in a way amenable for a scientific treatment."
The study is just one example of using the tools of physics to understand complex societal problems, Loreto says—a trend he thinks is only beginning. Statistical physics has also been used to study social hierarchies, crowd behavior, language dynamics and other social systems.
Such models are usually simplifications, however. The custody study analyzed a very basic system: Only heterosexual couples were included and complications such as parents who worked on certain weekends or exes who refused to cooperate were left out. Such drawbacks plague many applications of physics to social problems. "Whether statistical physics is going to let us understand something fundamentally new about social dynamics is still an open issue," says Santo Fortunato of Aalto University in Finland, who has reviewed studies using physics to model social dynamics. "Most results are still at the qualitative level. The main difficulty is in the validation of models—which require data on real social dynamics at an unprecedented level of detail—that only now is starting to become available."
Gomberoff himself admits that he still finds it easier to sit down with his exes and a calendar than to use his mathematical formula to plan his custodial arrangement. "The study is much more funny than practical," he says. The researchers do intend to expand their model to take on complicating factors, however. "Maybe in the future when people will live much longer and you'll have much more divorces, maybe the algorithm can have some utility."

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