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Beyond Black Swans: The Dragon Kings of Climate Change

Weird stuff happens. Sometimes really weird stuff happens. And sometimes freaky weird stuff happens–the kind of events that just don’t fit the imaginable.

Nassim Nicholas Taleb’s 2007 book Black Swan: The Impact of the Highly Improbable, had a huge impact on our understanding of weird and really weird events. The essence of Taleb’s Black Swan theory:

What we call here a Black Swan (and capitalize it) is an event with the following three attributes.

First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme ‘impact’. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

I stop and summarize the triplet: rarity, extreme ‘impact’, and retrospective (though not prospective) predictability. A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives.

The key to preparing for Black Swans rests in understanding the way events are statistically distributed over time. Unlike the normal distribution found in many phenomena, such as SAT scores, other phenomena follow what is known as a power law distribution, with many small events and few large events. Think forest fires. Black Swan provided a compelling account of the problem of over-relying on normal distributions to explain the world. For problems defined by “fat tail” power laws that have outlier events way out on the tail one would not find on a normal distribution, sooner or later an event at the end of that tail is going to hit, and it’s going to be big. So, planning for some policy problem based on a normal distribution can lead to under-preparation if in fact the problem follows a power law distribution.

Normal Power Law

Well, here’s the thing–it’s worse than that. A recent article by Didier Sornette of the Department of Physics and Earth Science at ETH Zurich, Dragon-Kings, Black Swans and the Prediction of Crises, discusses what he calls “life beyond power laws,” meaning “the existence of transient organization [of a system] into extreme events that are statistically and mechanistically different from the rest of their smaller siblings.” In short, he documents the existence of “genuine outliers,” events which don’t even follow the power law distribution. (In the power law graph shown above, sprinkle a few dots way out to the right of the chart and off the line.) The Black Swan event isn’t really an outlier, in other words, because it follows the power law and is simply an event way out on the tail. Genuine outliers violate the power law–they are even “wilder” than what would be predicted by the extrapolation of the power law distributions in their tails. A classic example is Paris–whereas all the populations of all other cities in France map well onto a power law, Paris is a genuine outlier. But Sornette documents that other such outliers exist in phenomena as varied as financial crashes, materials failure, turbulent velocities, epileptic seizures, and earthquakes. He calls such events Dragon Kings: dragon for “different kind of animal” and king to refer to the wealth of kings, which historically has been an outlier violating power law distributions of the wealth of their citizens. (Dragon Kings are also mythical Chinese shapeshifting deities ruling over water, as well as the name of some pretty good Chinese restaurants in cities around the U.S. according to Yelp.)

dragon king

So, what causes Dragon Kings? Sornette’s theory is complex, but boils down largely to instances when, for whatever reason, all of the feedback mechanisms in a system harmonize in one coupled, self-reinforcing direction. Massive outlier earthquakes, for example, are the result of “interacting (coupled) relaxation threshold oscillators” within the earth’s structure, and massive outlier financial crashes are the result of  “the unsustainable pace of stock market price growth based on self-reinforcing over-optimistic anticipation.”

What’s the lesson? The key to Dragoon Kings is that they are the result of the same system properties that give rise to the power law, but violate the power law because those properties have become arranged in such a way as to create severe instability in the system–a systemic risk of failure. When all feedback in the system has harmonized in the same self-reinforcing direction, a small, seemingly non-causal disruption to the system can lead to massive failure. As Sornette puts it: “The collapse is fundamentally due to the unstable position; the instantaneous cause of the collapse is secondary.” His assessment of the financial crash, for example, that, like other financial bubbles, over time “the expectation of future earnings rather than the present economic reality that motivate[d] the average investor.” What pops the bubble might seem like an inconsequential event in isolation, but it is enough to set the collapse in motion. “Essentially, anything would work once the system is ripe.”  And the financial system keeps getting ripe, and the bubbles larger, because humans are essentially the same greed-driven creatures they were back centuries ago when the Tulip Bubble shocked the world, but the global financial system allows for vastly larger resources to be swept into the bubble.

The greater concern for me, however, lies back in the physical world, with climate change. Sornette did not model the climate in his study, because we have never experienced and recorded the history of a genuine outlier “climate bubble.” But the Dragon King problem could loom. We don’t really know much about how the global climate’s feedback systems could rearrange as temperatures rise.  If they were to begin to harmonically align, some small tipping point–the next tenth of a degree rise or the next ppm reduction in ocean water salinity–could be the pin that pops the bubble. That Dragon King could make a financial crisis look like good times….


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