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Cataloguing the Causes of Collapse


Cataloguing the Causes of Collapse

As W.B. Yeats, Chinua Achebe and Jared Diamond have all famously noted: things fall apart. Collapse seems inevitable in any system, nothing lasts forever and entropy abounds in the universe.

A book by Bentley’s Charlie Hadlock, which won the university’s “Outstanding Scholarly Contribution” award, analyzes the specific types of collapse. A professor of mathematical sciences and Trustee Professor of Technology, Policy, and Decision Making, Hadlock had applied mathematical modeling to major environmental disasters such as Love Canal, Three Mile Island and Bhopal, and he had been a long-term risk analyst with management consulting firm Arthur D. Little, Inc. before coming to Bentley in 1990.

Hadlock’s book, Six Sources of Collapse: A Mathematician’s Perspective on How Things Can Fall Apart In the Blink of An Eye (The Mathematical Association of America, 2012), analyzes a wide range of both natural and man-made collapses, from the extinction of the passenger pigeon to the collapse of the financial markets to technological disasters.

Six Types of Collapse

Hadlock argues that there are six fundamental types of collapse, and that one or more of them is always at play in any given collapse. “I wanted to identify whether all these things happen because of some common cause or whether there were a variety of dynamics,” he says. “I started to sort collapses into categories and came to the conclusion that by using a mathematical framework as a language to describe these phenomena, I could classify all the collapses I was aware of into six different causes.”

Hadlock’s “six sources” are:

  • Low-probability events
  • Group dynamics/crowd behavior
  • Evolutionary processes in both natural and man-made systems
  • Instabilities
  • Non-linear processes
  • Network effects

“I try to provide six different lenses to look at risk, to give a ‘six-dimensional’ perspective on the risks of any given situation,” says Hadlock.

Low-probability events

Hadlock offers the tsunami that destroyed the Fukushima Daiichi nuclear power plant in 2011 as an example of a low-probability event, something that risk analysts and engineers thought so unlikely to happen that it had major catastrophic effects when it did. In the financial sector, low-probability events can cause collapses in long-term capital management systems, which sometimes underestimate and therefore don’t always guard against outlier events, focusing instead on normal outcomes. That’s all well and good, says Hadlock, until a low-probability event actually happens; then, unprepared systems can collapse.

Hadlock’s favorite example of a low-probability event having an outsized impact is in a photo he includes in his book. It shows a small deer hanging 60 to 80 feet off the ground in some power lines, which caused a major outage in Montana. The deer had been dropped there by an eagle. “You can’t really fault them for not planning for that,” he says.

Group dynamics / crowd behavior

Group dynamics or crowd behavior, says Hadlock, can lead to collapse when “somebody starts to do something, and all of a sudden everyone rushes to do the same thing, so that the event really gains magnitude—everyone’s leaning in the same direction at the same time.” A classic, Depression-era run on a bank is an example of group dynamics leading to the financial collapse of an institution, and this group dynamic also played a role in the Station Nightclub fire in Rhode Island in 2003, when everyone ran for the same exit even though others were available.

Evolutionary processes

Evolutionary processes can be understood by looking at the evolution of strategies used by students playing a game against each other, an exercise Hadlock conducts in his classes. “Over time, winners start to do better, and losers get eliminated and replaced by those with winning strategies,” he says. “After class I have students come up to me and say, ‘I never really thought about evolution this way,’ but it’s just the simple modeling and the application of a mathematical framework.” Hadlock also draws heavily on the work of scientist Jared Diamond to help illustrate ideas of evolutionary collapse for his students. “We do mathematical modeling based on his work in Guns, Germs, and Steel.”


Instabilities, says Hadlock, are often the “misunderstood and underappreciated, or even ignored, complexities of the ways systems work.” Hadlock cautions that we may currently be taking our form of government and “the stability of our whole system” for granted. However, given its complexities, “risks abound more than people might realize,” he says.

Non-linear processes

Non-linear processes and networks, Hadlock’s final categories, are often seen acting together as sources of collapse, he says. A classic example of a non-linear or disproportionate effect would be that of a single tree branch landing on a power line in western New York that causes an outage that ultimately blacks out the entire East Coast. The way our current power grid is constructed, says Hadlock, makes such collapses possible: the system is really good at doing what it’s designed to do in normal conditions, “but we keep discovering new failure processes in these complex systems when they are slightly perturbed.”

Another example of this effect is the way a single car with a flat tire even on the side shoulder of the highway can create a traffic back up that can last for hours. Highways are very good at moving cars along until one single small thing goes wrong, says Hadlock, “You’ll see no evidence of an accident or anything. It’s just the non-linear dynamics of the system,” he says. “You just pass a certain threshold of traffic, and something small goes wrong, and the whole thing gets gridlocked.”


Hadlock’s final category, networks, will be familiar to anyone who’s waited at an airport through delays or experienced a website going down. “Networks are very complex and everybody’s experienced network crashes at the airport, on campus, and elsewhere,” says Hadlock. “Networks crash even where the people who set them up assure us, ‘This could never happen.’” But the inherent complexity of a system makes it vulnerable to network collapse, whether we’re talking about technological networks or interpersonal networks, he says.


Hadlock admits that some of the implications of his work on collapse can be highly unsettling. But he feels the understanding and knowledge brought about by applying his six-dimensional thinking can be powerful. “We should not lull ourselves into complacency that we are not going to have to face the challenges of future collapses,” he says. “I try to provide these six different lenses so that we can take a less myopic view and be better prepared.”


by Meredith Mason  September 12, 2017

U.S. News & World Report ranked Bentley No. 2 among regional universities in New England and the Mid-Atlantic states, up from No. 3 last year, highlighting Bentley’s high-quality faculty and academic programs along with the strong value that students receive from a Bentley education.



The New York Post | October 17, 2017
Worcester Business Journal Online | October 16, 2017