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A Bahraini Shiite Muslim woman wearing a national flag holds a placard reading in Arabic 'Freedom for our prisoners of opinion' during an anti-government protest in the Manama coastal suburb of Karbabad on December 28, 2012. Bahrain has experienced unrest since early last year when authorities crushed protests led by the Shiite Muslim majority demanding a constitutional monarchy and greater rights.
SourceMohammed Al-Shaikh/Getty


Because statistics and calculus can’t tell you everything. But maybe complex mathematics can. 

By Joe Flood

We live in a mathletes’ day of big data and smart cities, when computer models and cutting-edge algos promise to make the world an ever more explicable, predictable place. And yet we’re also inundated with all kinds of crises that few saw coming and even fewer know how to deal with: the financial crisis and European debt debacle, terrorism, civil wars, Ebola.

That’s where Yaneer Bar-Yam comes in. Known in nerd circles as the man who predicted the unrest that became the Arab Spring, Bar-Yam is one of the luminaries in the emerging field of “complex systems” mathematics — and he did literally write the (text)book on it. He’s also the founder of the New England Complex Systems Institute (NECSI). From his office in Cambridge, Massachusetts, Bar-Yam joined OZY to explain what complex systems are, why traditional mathematics falls short and what mortgage loans have to do with ISIS. 


What does the Complex Systems Institute do?

Yaneer Bar-Yam:

A lot of our research is on global crises: the financial crisis, the food crisis, the Ebola epidemic, to name a few. We seem to have a lot of them these days. It has to do with how the changing global connectivity is affecting global vulnerability.



Why do we need a special field of math for this?


Complex systems science is about what’s beyond the traditional mathematical tools of science — calculus and statistics. Statistics assumes that things are generally independent and relies on averages. Calculus assumes things are smooth. Averages are fine if things are independent all the time, but they just don’t work when variables shift from being independent to dependent. And dependencies in a system can cause rapid changes in behavior, like cascades — that’s not a smooth change. Dependencies violate both statistics’ assumptions and calculus’s assumptions, so we need very different tools for addressing them. 


You’ve brought up phase changes as an example of where traditional math falls short — like when substances transition from liquid to gaseous form. So we have statistics that work for liquids, statistics that work for gas …


But the transition [stage] is very different in its behavior. There’s a very particular way that certain transitions happen. That’s where physicists discovered this breakdown of calculus and statistics. In trying to figure out why that was the case, it was necessary to come up with an entirely different mathematics. Statistics and calculus are incredibly powerful tools, but their power sometimes blinds us to what more needs to be done. 


NECSI’s studies often look at how small changes in one system can cause huge, unpredicted consequences around the world. Do you have any good examples of this?


One example is the financial crisis. It started in the mortgage market and then cascaded into the stock market. People moved their money out of the mortgage and stock markets and into the commodity markets. The commodity markets then went through bubble-crash dynamics and then an oscillation — which caused food riots around the world. There was a second oscillation, and the Arab Spring occurred in that moment.

So there’s a very strong connection with this amazing cascading event [the mortgage crisis], which cascaded from mortgages to other financial instruments — and then to food and then to social unrest and a lot of political instability. Which continues because what we see now, of course, is the amazing disruption that happened in Syria and led to ISIS. That is all an extension of the financial-crisis cascade. 


Can complex systems dynamics help with something like the response to Ebola? 

A Liberian health worker speaks with families in a classroom that was used as Ebola isolation ward in August, 2014 in Monrovia, Liberia. During this time the Ebola epidemic had killed more than 1,000 people in four West African countries.

A health worker speaks with families in an Ebola isolation ward in August 2014 in Monrovia, Liberia. 

Source John Moore/Getty


Existing approaches to thinking about epidemics are based largely on past events. We didn’t think that would work here: Last year’s Ebola outbreak was 10 times the size of the previous one, so using statistics to anticipate the next set of events was surely not going to work. 

Early on, health strategies focused on contact tracing, which had worked in past outbreaks. But once there were more than a few cases in urban areas, contact tracing just wasn’t effective. You can’t find all the contacts — you don’t have the info or capacity to trace them all. So we advocated very strongly for an approach based on community-level monitoring: screening everyone in a community for fevers and starting isolation.

We eventually talked to people in Liberia about this in the beginning of October. As we talked to them, we found out that they had done this starting in mid-September, and that’s when the new cases had started to decline. It took until mid-December for the screening policy to move to Sierra Leone. And if you look at the pattern of cases in Sierra Leone, it was going up and up, and then in mid-December, it started going down. We now understand community screening as an effective policy for large outbreaks.

The upshot is that we need to understand, structurally, how connectivity in a system relates to the disease propagation. That, in turn, will enable you to also understand which strategies will work and which strategies won’t. It must become part of the policy process.

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