Tag Archives: Complex Systems

Beware The Long Tail – Science News

… Occasionally crashes are so large that they are outliers even from the power law distribution, says Didier Sornette of ETH Zurich. Their specialness makes them predictable, says Sornette, who calls the standout events “dragon-kings.

Sornette and his colleagues argue that understanding dragon-kings [very large crashes] may help economists spot markets teetering toward crashes. Out-of-control growth can be one sign of an approaching dragon-king. When herding behavior among investors amps up, a stock’s or index’s growth rate can increase faster than exponentially, leading to more herding, Sornette says. This positive feedback among investors, the same sort of feedback that concentrates the wealth of kings, brings the system to a tipping point. About two-thirds of the time, a crash results, Sornette wrote in a 2009 paper online at arXiv.org.

Beware The Long Tail – Science News

Mitigating disasters by hunting down Dragon Kings: Forecasting natural or economic disasters by identifying statistical anomalies

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This review focuses on elucidating how Dragon Kings are created and can be detected. It also gives an overview of their empirical evidence in abnormal rainfall, hurricanes, and sudden events such as landslides and snow avalanches. The authors also outline the limitations of this sort of statistical analysis. For example, despite being sometimes interpreted as featuring characteristic events of Dragon Kings, great earthquakes may not be formally confirmed as such.

Finally, the authors share their views on the importance of devising prediction models that could become the basis for Dragon Kings simulators. These could be designed to help interpret the warning signs of complex systems evolving from their safe equilibrium into extreme events such as the subprime crisis, and to steer them into sustainability and ultimately avoid such crisis.

Mitigating disasters by hunting down Dragon Kings: Forecasting natural or economic disasters by identifying statistical anomalies

Dragon-Kings, Black Swans and the Prediction of Crises

Dragon-Kings, Black-Swans and Prediction

How To Identify The Tipping Point In Any System

This is Jerry McManus’ follow-up to his very insightful article, Modeling Collective Behavior, and it delves into the scientific meaning of a commonly-used, but sometimes misunderstood term of complex systems theory – “tipping point”. I have briefly added to his discussion of tipping points in forest ecosystems and financial systems by referencing a recent report produced by Goldman Sachs on the Eurozone crisis (marked within the text). Other than that, it’s all Jerry! So, without further ado…

Modeling Tipping Points


The term “tipping point” crops up frequently, especially in discussions of world events such as financial collapse and climate change. Like the word “sustainable” which gets used with increasing abandon, and often with little thought to the actual meaning of the word, so too the term tipping point can be elusive and used in contexts where it may or may not be suitable. I’ve probably been guilty of this myself, but recently my thinking on the subject has been greatly clarified and I hope to pass on what I’ve learned about what does, and does not, constitute a tipping point.

We will look at a couple of simple models that explore tipping points in an attempt to think more clearly about the problems of financial contagion and climate change, but first we must try and nail down a working definition of tipping points.

How To Identify The Tipping Point In Any System

The mathematical law that shows why wealth flows to the 1% | The Guardian

The economist Edward N Wolff, of New York University, has pointed out that, as of 2007, the top 1% of households in America owned 34.6% of all privately held wealth, and the next 19% had 50.5% of the wealth. This means that just 20% of the people owned 85% of the wealth, leaving only 15% for the bottom 80% of the people. No one who is interested in an equitable society can fail to be irked by this unfairness.

But the unfairness is, unfortunately, not unexpected. What the protesters are fighting (consciously or unconsciously) is the 80/20 rule – variously called Pareto’s principle, Zipf’s law, the long tail or Benford’s law, depending on what you are studying – a staple in scientific, economic and business textbooks, the go-to idea to show how the frequency of a set of natural events is not always what you might recognise as, well, natural.

The maths underlying the 80/20 rule, known as the power law distribution, is found in many natural systems over which no single human has much influence. Its concentration of the extremes seems built into the fabric of complex systems that depend on numerous factors that continually change over time.

The mathematical law that shows why wealth flows to the 1% | Alok Jha | Comment is free | The Guardian

Welcome to the Age of Instability

As Nassim Taleb of “black swan” fame has explained, it is misleading to say the last few grains of sand on the debt pile, for example, subprime mortgages in the housing bubble, are responsible for the entire sand pile collapsing: the masking of risk was systemic, and thus the sand pile was doomed to collapse regardless of the nature of the final few grains of sand.

Similarly, it won’t really matter what the final trillion dollars of Federal debt was borrowed for; the default/collapse of the government debt pile is inevitable.

In betting the farm to prop up a façade of financial stability, the Federal Reserve and the Federal government have doomed the entire system to collapse. Taleb explained why in the June 2011 issue of Foreign Affairs: “Complex systems that have artificially suppressed volatility become extremely fragile, while at the same time exhibiting no visible risks.” That describes the global economy in 2007, just before the financial meltdown of 2008 “surprised” conventional economists and Wall Street apologists.

As Taleb has explained, the very act of suppressing fluctuations renders systems extremely prone to large-scale disruptions that are viewed as low-probability events, the infamous “black swans.”

charles hugh smith-Welcome to the Age of Instability

A Contagion of Black Swans – TheStreet

Risks of more and repeated Black Swans, previously perceived to be small by corporations, investors, politicians and regulators, should now be reassessed, owing to (among other issues) globalization, tighter correlations, advancements in technology, the growing/excessive complexities of interlocking supply chains and derivatives, the acceptance of greater/extreme risk-taking (Minsky’s moment: “the longer people make money by taking risk, the more imprudent they become”), the greater connectivity of increasingly more complex systems (see Paul Ormerod and Rich Colbaugh’s “Cascades of Failure and Extinction in Evolving Complex Systems”) and so forth. I see a greater and more dynamic instability is the new normal. Witness the increased regularity of economically, politically and socially altering Black Swan events over the past decade (Note: three of the eight deadliest natural disasters in the last century have occurred since 2004):

Kass: A Contagion of Black Swans – TheStreet

If a decision you make is like a grain of sand dropping onto a sandpile, then modern society forces the grains to drop at a faster rate. You are forced to make more and more decisions each day because of how you are bombarded with messages through TV, radio, internet and other media. Modern society also makes the grains of sand more sticky. So our grains of sand and sandpile are grains of sticky rice and a rice pile respectively in modern society. Today’s interconnectedness means that more people are able to influence the decisions of others. The amount of influence represents stickiness with more influence equaling more stickiness.

The effect of dropping grains faster and making them more sticky means that the rice pile will build up faster and steeper. It moves to a pre-crash state much more quickly than in the past. This results in black swans happening much more frequently than in the past.

Niall Ferguson On Whether The Financial Crisis Will Lead To America’s Decline [Videos]

The topic once again is the Financial Crisis, and specifically how, why and whether it will lead to America’s decline. Of particular note is Ferguson’s spot on characterization of the primary deficiency in the so-called brains of economists, namely that they see patterns, equilibria and stable systems where there are absolutely none: i.e., in the complex (as in Lorenzian) world of economics: “Complex systems look like they are in equilibrium, but they are not: they are constantly adapting, highly decentralized, interdependent systems and this process of adaptation can continue for quite a long time. And you think to yourself when you look at it, that’s in a wonderful equilibrium. That’s how we think about the economy. That is how economists teach economics. They talk about it in terms of equilibrium. The bad news is that in fact we inhabit a complex system that has virtually nothing to do with the neoclassical model that you are taught in Econ 101. And that’s why the economists failed to predict the financial crisis… For me American power if you generalize beyond the realm of finance through the geopolitical system is a perfect example of a highly complex system which looks like it is in equilibrium but like all the great empires of the past is quite close to the edge of chaos. And our nightmare scenario should be that something happens to us like happened to the Soviet Union… It suddenly just falls apart. And I think the trigger, the catalyst if you want to switch to chaos theory the butterfly in the tropical rainforest that flaps its wings and posits the distant thunderstorm is going to be the credibility of fiscal policy. That just seems to me like the obvious place where things can turn nasty, and they turn nasty with amazing speed.”

Niall Ferguson On Whether The Financial Crisis Will Lead To America’s Decline And A Glimpse Of The “Post-Pax Americana” Dark Ages | zero hedge

Why Wars Follow the Power-Law Distribution

The regularity of conflict in general poses a question Can we explain wars as self-organizing criticality?

Lars-Erik Cederman Modeling the Size of Wars: From Billiard Balls to Sandpiles

Cederman graphed the casualty rates of interstate war using the COW dataset from 1820 to 1997 and Jack Levy’s dataset of Great Powers conflicts from 1495-1965. The results from both datasets show a strong correlation with a power law.

Cederman offers a hypothesis to describe this constant empirical pattern. First, the definition of self-organizing criticality:

Self-organized criticality is the umbrella term that connotes slowly driven threshold systems that exhibit a series of meta-stable equilibria interrupted by disturbances with sizes scaling as power laws. In this context, thresholds generate non-linearities that allow tension to build up. As the name of the phenomenon indicates, there has to be both an element of self-organization and of criticality. Physicists have known for a long time that, if constantly fine-tuned, complex systems, such as magnets, sometimes reach a critical state between order and chaos.

In other words, this produces the cyclical patterns of war. There is a relatively stable punctuated equilibrium, followed by outbreaks of conflict outside of equilibrium. War is a phase transition.

Power-laws of War « Net Wars

Empires on the Edge of Chaos – Big Idea

The Centre for Independent Studies 2010 John Bonython Lecture with Niall Ferguson.

Is the rise and fall of empires cyclical or arrhythmic? How does economic profligacy – whether the result of arrogance or naivety – contribute to the downfall of civilisations?

Today Professor Ferguson will argue that great powers or empires are in the strict sense of the word, complex systems. Made up of very large numbers of interacting components that are quite asymmetrically organised. In other words, he continues, their construction more resembles a termite hill than an Egyptian pyramid. They operate somewhere between order and disorder. Moreover imperial falls are nearly always associated with fiscal crises, when there are dramatic imbalances between revenues and expenditures.

Thus alarm bells should be ringing in Washington DC but what does that for mean for Australia?

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Empires on the Edge of Chaos – Big Idea – 22 August 2010