Complex Systems Science: How Do Math And Intuition Help Us Understand Whole Systems?

There I sit, gulping a latte. How did he figure out where to go?

"t's an interesting kind of search problem," he says. "It just seemed like the right place to go. I figured you wouldn't be hanging out with the students, and that coffee might have something to do with this. I was right."

That kind of intuitive problem solving, he thinks, is not simple to explain and even harder to replicate with a computer. It's way beyond the best artificial intelligence programs, and it would be charitable to say that neuroscience has a firm grasp of how the brain manages such a task. But it's not magical either.

"It's complex," he says.

And complexity lies at the heart of Dodd's research and teaching as an assistant professor of mathematics and statistics. He's part of a group of researchers who make up UVM's Complex Systems Center launched in 2006 by the College of Engineering and Mathematical Sciences.

"In its most simple form, a complex system is many distributed parts interacting in some distributed way," Dodds says, "giving rise to some interesting, often unexpected, macrophenomena." Take a neuron. Alone, it's a cell that conducts a chemical signal. But billions together, each woven with thousands of links that adapt and change over time, emerge as a brain capable of following a hunch and the smell of coffee.

Big Band, no conductor

While the human brain may be the ultimate complex system, other examples appear everywhere. Take army ants. Despite their name, they have no general, and their queen sends out no instructions. No ant is aiming to get across that gully, and there is no blueprint or traffic light. Yet millions of ants, following the same instinctive rules of individual behavior, can build bridges with their bodies and forage for food along vast efficient highways.

"That's emergence," says computer scientist Maggie Eppstein, director of the UVM Complex Systems Center. "You can't just look at the rules each little thing is following and then describe what is going to happen in the whole system. You've got to run the model or observe the whole to understand what happens at the next scale."

Ferociously chaotic air currents resolve into a tornado that moves across the landscape maintaining its form. "In complex systems, through local interactions and self-organization, stable or semi-stable patterns emerge at a next level or a higher scale," she says, "but they are difficult to predict because they are so sensitive to small changes in the system or initial conditions."

Applying insights like these, Eppstein and her colleagues across the university are helping to lead the rapidly developing field of complex systems science. They aim to bring new approaches to some of the world's most vexing problems like improving hurricane forecasts, understanding the effects of phosphorus pollution in a watershed, slowing the spread of invasive species, making robots that can start to discern the intentions behind an action, and untangling the genetic and environmental threads that lead to heart disease.

The lights are on

Recall what happened on the afternoon of Aug. 14, 2003. In a cascade, the lights went out in Cleveland, New York City, Baltimore, Albany and Detroit. Eventually, more than 50 million people were without power across the Northeast and Canada as 265 power plants shut down.

This famous blackout was a complex systems failure. No one pulled the plug; numerous local problems and mistakes created a series of dynamic feedback loops. The result: an unpredictable regional disaster.

"Nobody's in charge of the electric grid," says Paul Hines, a power engineer who is part of the UVM complex systems group, "there are hundreds of companies and entities who all have a role. What's amazing is that in the midst of this system, with millions of human and non-human actors — a lot that we can't predict — we still get order. Most of the time, when you flip the switch, you get light."

Or, as Dodds says, complex systems are "typically highly balanced, flexible, and robust, but are also susceptible to systemic collapse."

Decades of work to improve overall control of this patchwork of operators, powerplants, substations, and transmission wires — a product of history more than rational design — haven't gotten very far. "The reliability of the grid has basically been constant for the last 25 years," Hines says. He recently presented data that shows the frequency of blackouts has remained the same since 1984, and also that very large blackouts are more frequent than would be expected from traditional exponential statistics and risk assessments.

"Traditional methods have tried to estimate the reliability of the system by taking each component individually," Hines says. Any one substation is pretty straightforward and may not appear to be hard to manage. "But this misses what happens when combinations of components fail," he says.

In a complex system, one plus one might add up to a lot more than you'd guess. These kinds of nonlinear interactions don't show up in a static model that simply describes the electric grid. Which is why Hines is developing dynamic graph-based models instead that draw on new methods from network theory.

"Our goal is not to create a complex model, our goal is to create a useful model," he says, "a simple model that helps us understand a complex system." He's feeding data from actual power systems into his model, seeking sets of components that cluster together when he runs the model since these may be particularly important to maintaining the robustness of electricity delivery systems.

Parts is not parts

"Complex systems science is just the evolution of science," Dodds says. Since the revolution that Newton and Descartes helped launch, the main thrust of so-called normal science has been to look for smaller pieces and more fundamental laws. Molecules yield atoms yield quarks.

"There are many problems that we figured out by breaking things into little pieces," Dodds says. "Scientists figured out DNA with its double helix. And then they figured out the human genome by measuring like crazy. There was a sense conveyed that once we understood all the bits of the genome, we'd understand everything human," he says, "but that's totally insane."

"It's like saying once we understand atoms we understand matter," he says, "But we don't."

Of course, many of the underlying ideas behind complex systems are far older than the name. It was Aristotle who stated that the "whole is more than the sum of the parts." But complex systems science takes this realization further. As physicist PW Anderson wrote in a seminal 1972 paper in Science, in a complex system “the whole becomes not only more than, but very different from the sum of its parts."

"The ability to reduce everything to simple fundamental laws does not imply the ability start from those laws and reconstruct the universe," Anderson wrote.

Peter Dodds stands at the bottom of the Davis Center stairs and watches students playing pool. One after the other, they rub their cue sticks with chalk and lean over the table. "If you want to understand how humans behave collectively you have to understand what their psychology is: and you will never get that from studying quarks or DNA or cells," he says, as a stream of students pass around him like he's a rock in a river. "Never."