Category Archives: Power_Law

How to Predict State Failure | Nassim Nicholas Taleb and Gregory F. Treverton | Foreign Affairs

But Syria’s biggest vulnerability was that it had no recent record of recovering from turmoil. Countries that have survived past bouts of chaos tend to be vaccinated against future ones. Thus, the best indicator of a country’s future stability is not past stability but moderate volatility in the relatively recent past. As one of us, Nassim Nicholas Taleb, wrote in the 2007 book The Black Swan, “Dictatorships that do not appear volatile, like, say, Syria or Saudi Arabia, face a larger risk of chaos than, say, Italy, as the latter has been in a state of continual political turmoil since the second [world] war.” ?

The divergent tales of Syria and Lebanon demonstrate that the best early warning signs of instability are found not in historical data but in underlying structural properties. Past experience can be extremely effective when it comes to detecting risks of cancer, crime, and earthquakes. But it is a bad bellwether of complex political and economic events, particularly so-called tail risks—events, such as coups and financial crises, that are highly unlikely but enormously consequential. For those, the evidence of risk comes too late to do anything about it, and a more sophisticated approach is required.?

Nassim Nicholas Taleb and Gregory F. Treverton? | How to Predict State Failure | Foreign Affairs

Thoughts from the Frontline – On the Verge of Chaos

“There are some geopolitical thinkers I respect who argue that all this could trigger a regime change in Russia. And others who argue that it will make Vladimir Putin even stronger and that he will want to double down on his policy of destabilizing Ukraine sooner rather than later. Putin does not strike me as being willing to step aside in the manner of a Boris Yeltsin. I doubt he will go gently into that good night. He is a wildcard on the geopolitical stage.”

The “this” referred to above is about low oil prices and the fact that China will be devaluing its currency soon. That big energy deal between Russia and China is in yuan. If China is forced to devalue its currency in order to respond to Japan, then that is going increase pain on Russia.

Concerning Russia, there is a threat of regime change, instability plus limited options. Sounds like revolution will soon enough start brewing in Russia unless Putin can somehow redirect everybody’s attention. And truly Putin is not kind of guy (so far) that is likely to go quietly in the night. Things are more likely to get worse before they get better.

Thoughts from the Frontline – On the Verge of Chaos [Excerpt]

Complexity and Collapse

Okay class, for those who want a little extra credit, I’m going to give you some extra reading and viewing. Lacy Hunt encouraged me to listen again to our friend Niall Ferguson’s speech entitled “Empires on the Edge of Chaos” (Note: the introduction is 10 minutes long and can be skipped. You know who Niall is. And there is considerable Q&A at the end, so the speech itself is roughly 40 to 45 minutes. But the Q&A has lots of laughs, which makes it worth it.) Or you can read this article by Niall in Foreign Affairs, which has much of the same content.

I want to repeat the two quoted paragraphs that opened this letter, along with one more from the Foreign Affairs article. (Again, all emphasis mine.)

Great powers and empires are, I would suggest, complex systems, made up of a very large number of interacting components that are asymmetrically organized, which means their construction more resembles a termite hill than an Egyptian pyramid. They operate somewhere between order and disorder – on “the edge of chaos,” in the phrase of the computer scientist Christopher Langton. Such systems can appear to operate quite stably for some time; they seem to be in equilibrium but are, in fact, constantly adapting. But there comes a moment when complex systems “go critical.” A very small trigger can set off a “phase transition” from a benign equilibrium to a crisis – a single grain of sand causes a whole pile to collapse, or a butterfly flaps its wings in the Amazon and brings about a hurricane in southeastern England.

Not long after such crises happen, historians arrive on the scene. They are the scholars who specialize in the study of “fat tail” events – the low-frequency, high-impact moments that inhabit the tails of probability distributions, such as wars, revolutions, financial crashes, and imperial collapses. But historians often misunderstand complexity in decoding these events. They are trained to explain calamity in terms of long-term causes, often dating back decades. This is what Nassim Taleb rightly condemned in The Black Swan as “the narrative fallacy”: the construction of psychologically satisfying stories on the principle of post hoc, ergo propter hoc.

Defeat in the mountains of the Hindu Kush or on the plains of Mesopotamia has long been a harbinger of imperial fall. It is no coincidence that the Soviet Union withdrew from Afghanistan in the annus mirabilis of 1989. What happened 20 years ago, like the events of the distant fifth century, is a reminder that empires do not in fact appear, rise, reign, decline, and fall according to some recurrent and predictable life cycle. It is historians who retrospectively portray the process of imperial dissolution as slow-acting, with multiple overdetermining causes. Rather, empires behave like all complex adaptive systems. They function in apparent equilibrium for some unknowable period. And then, quite abruptly, they collapse.

The single most commented-upon letter that I have written was called “Fingers of Instability.” Longtime readers know it well, and I would suggest new readers take the time. It contains extremely important concepts for understanding why financial markets can advance smoothly for so long, and then all of a sudden there is chaos. The fingers of instability distributed throughout the sand pile of the global economic system end up getting triggered by some event that may in itself be quite minor. Yes, there are many factors contributing to an unstable global sand economic pile (think massive global debt, wanton overleverage, mischievous central banks with immoderate views of their importance, etc., etc.), but it only takes that fateful final grain of sand, dropped on just the right spot in the pile, to bring the whole thing cascading down.

What Niall is talking about is something that goes far deeper than another financial crisis like the one we recently experienced. What he is pointing out is that countries in financial distress are more constrained than normal in their actions. They have less ability to respond to crises. And some countries in crisis react in very unpredictable ways. Let’s talk about a second-order problem stemming from the fact that Japan is doing what it feels is necessary to keep from suffering a deflationary collapse. Understand, I’m not being critical of the Japanese for taking the actions they have, because I simply don’t know what other choice they have. That’s what makes their situation so difficult.

Japan’s major economic competitors – Germany, Korea, and China – will all have to respond, or their businesses will lose competitive advantage. Okay, we have seen large-scale currency movements all our lives. We adjust. That’s what businesses do.

Except, China and Russia have just signed an agreement for Russia to export rather massive amounts of energy to China, and they will take payment in yuan rather than dollars. A yuan that is going to be falling in value against the dollar as China responds to Japan.

In an ideal world for Russia, the Russian central bank would simply take the Chinese currency and add it to their reserves. But that would trigger a rather large “oops” that was not in the equation when they signed that deal. The yuan they are going to get is going to be losing value on the international market, and Russia is going to need hard currency (i.e. dollars) to pay down its large dollar-denominated debt and buy equipment to maintain and increase its ability to produce energy. And that equipment is generally sold in dollars and not in renminbi.

Couple that situation with the real potential for oil to go below $70 and Russia would have significant budgetary problems. And as David Hale pointed out recently in a private letter, if the US and Iran actually settle their differences over nuclear armaments later this month and sanctions are lifted, that could bring another 1–1.5 million barrels of oil a day onto the world energy markets. (He suggests it would have the same effect as a $400 billion global tax cut.) Mexico is committed to increasing its output, as are other countries, including the US. Sub-$70 oil is not out of the question, and in a global recession we could touch $50 easily. And while that would be good for consumers everywhere, it would certainly put a strain on Russia and other oil-producing countries. In fact, the scenario portends a major crisis for Russia.

And while we’re not as worried about Venezuela or other smaller oil producers, Russia is a potential problem, simply because it is so unpredictable. As noted above, the Japanese population is willing to take a great deal of pain. I don’t think we can say the same thing about the Russians at this point.

There are some geopolitical thinkers I respect who argue that all this could trigger a regime change in Russia. And others who argue that it will make Vladimir Putin even stronger and that he will want to double down on his policy of destabilizing Ukraine sooner rather than later. Putin does not strike me as being willing to step aside in the manner of a Boris Yeltsin. I doubt he will go gently into that good night. He is a wildcard on the geopolitical stage.

Russia has been willing to let the ruble fall rather precipitously rather than supporting it with their dollar reserves, which they are saving for other purposes. Even though the Russian economic situation is deteriorating due to sanctions, the Russian people have so far seemed to tolerate the downturn. As noted in last week’s Outside the Box, the West in general and the US in particular are blamed for Russia’s woes multiple times daily in the Russian media. Given the unpredictability of the current Russian leadership, there is simply no way to guess the outcome. That should make you nervous.

The Fragile Eight

The 2008 crisis demonstrated that the global economic system is far more connected than most imagined. There has been no real deleveraging since that time as nations everywhere have doubled down on deficits and debt. European banks are just as leveraged to sovereign debt as they were before the crisis hit.

The recent Geneva Report on global deleveraging highlighted what the authors termed the “fragile eight” countries of Brazil, Chile, Argentina, Turkey, India, Indonesia, Russia, and South Africa as an “important source of concern in terms of future debt trajectories.” China and the “fragile eight” could find themselves in the unwanted role of hosts to the next phase of the global leverage crisis, it warned.

The accumulation of household, corporate, and government debt in both the emerging and developed worlds has been made all the more troubling by stubbornly low and slowing growth rates. The global capacity to take on more debt is rapidly diminishing because of the combination of low growth and low inflation, if not outright deflation, that we are beginning to see in major countries.

There seems to be a stubborn unwillingness on the part of authorities to recognize the problems that come along with swelling sovereign debt. We are coming ever closer to the point at which countries are going to have difficulty raising debt at interest rates that makes sense, absent the ability to create a shock and awe campaign like Japan’s. And few countries (actually, none come to mind) have the ability to monetize their debt to the tune of 200% of GDP, as Japan is setting out to do, without causing a dramatic currency collapse.

I have this argument all the time with fellow analysts. I get that “austerity” in a deflationary or even disinflationary environment is not exactly pro-growth. And if a country’s debt is low and there is growth, then you can get away with increasing debt. But there is a limit to the amount of debt that a country can take on, and we are approaching it in country after country. This trend is not good for global economic growth or stability. The second-order unintended consequences, such as those Niall describes, are very difficult to contemplate.

The world is not going to come to an end. I will be writing this letter and hopefully you will be reading it in 10 years. But economies and markets are going to get more fragile and volatile in the meantime. This is not the time to be a full-throated bull in the equity markets. And given the potential dollar bull market, there is going to be pressure on most commodities. Corporate debt, especially high-yield debt, is priced for perfection. When I look out over the horizon, I simply don’t see perfection. At a minimum, you should not be long high-yield debt. And if you’re running a business, you should get all the debt you can, even if you bank the cash, at today’s low rates for as long a term as you can get it. Take advantage of this unbelievably forgiving debt environment.

Thoughts from the Frontline – On the Verge of Chaos

Making Progress in Earthquake Prediction

In the days before the 2011 Tohoku quake and tsunami, which killed more than 18,000 people, seafloor instruments showed that the offshore fault responsible was chattering and slipping slowly. Similar slip preceded a quake on an offshore fault in Chile.

Those tantalizing hints led two respected earthquake experts to suggest in an opinion piece in the journal Science that better monitoring of the seafloor might someday identify reliable precursors to the world’s most destructive quakes — including the one that will strike someday off the coast of the Pacific Northwest.

“Whether earthquakes are predictable or not is still an open question,” wrote Emily Brodsky and Thorne Lay, of the University of California, Santa Cruz, “but perhaps there is now some cause for optimism.”

Japan hangs on to goal of earthquake prediction | The Seattle Times

Shortly before the 2011 tsunami in Japan “the offshore fault responsible was chattering and slipping slowly.”

Since this blog is more about war than anything else, why am I concerned about earthquake prediction? Because wars and earthquakes are similar mathematically. They both work the same way. If I can better understand how to predict earthquakes then that might help in predicting wars. In this case the article confirmed what I pretty much already knew: A system will reached an unstable tipping point shortly before a crash. Recognizing that you have reached an unstable tipping point is the key to understanding that a crash is coming.

A tipping point is reached when something small can cause something big. In the case of earthquakes, normal earth movement will start to become amplified. At this point there is no big collapse yet but it is near. The area has reached a tipping point. Having plenty of remote sensors can help detect these abnormal movements.

In the case of war, think about what it would take for Russia and/or China to go war against America. We know for sure that one tiny little incident could easily blow up into a major war between China and America. Clearly China and America are at a major tipping point. There is zero doubt about that.

What about Russia and America?

It´s harder to see with Russia and America. Putin threw out some implied nuclear threats the other day if anyone messes with Russia. Presumably it would be over Ukraine. Russians leaders have thrown out quite a few nuclear threats since 2008. What would happen if America and Nato started helping Ukraine? What would happen if Nato started stationing troops in the Baltics? It´s possible that things could get out of hand. Also, the West is sanctioning Russia sending its economy toward the direction of a recession. And a recession could mean big trouble for Putin.

It appears that Russia and America are entering a tipping point but it´s not quite as sensitive as the China-America tipping point at this time. Given the western sanctions on Russia, in a couple of years the Russia-America tipping point could be just as sensitive as the China-America one.

Are Financial Crashes Just Like Earthquakes? – NASDAQ.com

There are countless methods of predicting what will happen next in the stock market. Technical traders have their charts, quant funds use specialized algorithms, and psychics have crystal balls. Many of their methods have failed quite spectacularly in the past, especially in the 2008 financial crisis.

With that in mind, researchers have turned to other methods of understanding the vagaries of financial markets. One idea is to model the market’s activity in the same way geophysicists model earthquakes. It seems to work, but what if it ends up working too well?

Seismic financial activity
The idea is that a financial market crash looks — mathematically speaking — kind of like an earthquake. Both tend to be self-perpetuating, meaning that they build on their own momentum, and are often followed by aftershocks. Indeed, the researchers found that between 84% and 88% of extreme market drops were caused by this “self-excitation.”

Also common to both is that extreme negative events are more common than normal statistical models would suggest, and in both cases, it’s these extremes that beget the biggest risks. In other words, it’s not the 3.0 magnitude quake that’s going to worry you, it is, as we Californians like to call it, The Big One.

Are Financial Crashes Just Like Earthquakes? – NASDAQ.com

And as I have said many times in the past, they are like wars too. If you think about financial crashes and wars as like earthquakes, then it frees up the mind. You will not remain stuck on stupid by thinking the future is just a linear projection of the past. These crashes don´t follow the normal distribution. They follow the power law distribution which has a nice, big, fat tail. Lots of room for big crashes. Also, the possibility of a great-power nuclear war opens up. It´s just a really big crash.

How To Analyze Black Swans

“Modeling crises in this way puts a premium on context and not just collection.”

And the consequences of all this for intelligence analysts? It fundamentally changes the question we ask ourselves. It suggests we should focus less on the grains of sand and what impact they will have on the sandpile and spend more resources trying to understand the sandpile itself.

Consider the current crisis in Crimea. It is tempting to watch each news report as it rolls in and to speculate on the effect of that piece of news on the crisis. Will it make it worse or better? And to what degree?

But what of the sandpile? Is the Crimean crisis in a critical state or not? If it is, then it is also in a state where a black swan event could arise but the piece of news (i.e. particular grain of sand) that will cause it to appear is unpredictable. If not, then perhaps there is more time (and maybe less to worry about).

We may not be able to tell decisionmakers when the pile will collapse but we might be able to say that the sandpile is so carefully balanced that a single grain of sand will, eventually, cause it to collapse. Efforts to alleviate the crisis, such as negotiated ceasefires and diplomatic talks, can be seen as ways of trying to take the system out of the critical state, of draining sand from the pile.

Modeling crises in this way puts a premium on context and not just collection. …

Sources And Methods: How To Analyze Black Swans

If the global order is represented by one sandpile, then the regional order represents a subset of the global order sandpile. Regional instability means one section of the bigger sandpile is unstable. A collapse of a region might not affect the bigger sandpile. However, if the bigger sandpile has been relatively stable for a long time, meaning a lot of sand has built up everything to new heights, then one or more regional collapses could bring down the entire pile.

The geopolitical context we are looking for is represented by the time of stability (sand height), rigidity (stickiness) and connectiveness. Rigid, stable systems will eventually collapse. Connectiveness between areas allows the collapse to be transmitted to other areas.

Currently there is instability in the Middle East, Asia and Eastern Europe. The global order has been in existence a long time – since the end of World War II. Trade (connectiveness) between countries is near an all-time high, but now starting to fall.  The world’s leading empire, the US, is now in decline. People are now openly discussing the possibility of war between the US and Russia, and the US and China. Both Russia and China are forming a military alliance, but they deny it (what did you expect?). The US is using trade to punish Russia and discussing the possibility over China. It appears that a small event in any of the three regions could lead to a major war – each of the regions is ready for a full-scale collapse. Apparently, the bigger sandpile is now at risk of collapse.

 

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

If you are upset with the wealth distibution in the country, then welcome to the 80/20 rule. The 80/20 rule is really a mathematical law – the power law. It is this law, and not you, that gets to define the wealth distribution all over the world. Basically, the law says that 20% of the people will own about 80% of wealth. Pretty unfair, no? But that’s the way it is. Oh, I forgot to mention. This distribution is not optional. If you seek to change it (violate a mathematical law), there will be negative consequences.

The 80/20 rule roughly applies to things where some kind of feedback loop drives everything forward. This is where the past heavily influences the future. In situations where the past heavily influences the future, then the 80/20 rule will fall out.

Take a look at this video showing the unfair wealth distribution in America. You probably won’t be so shocked now that you know the 80/20 rule.

Wealth Inequality in America

One of the main issues raised by the Occupy demonstrators is the inequitable distribution of wealth. Their slogan focuses on the extreme difference between the richest and the poorest: “We are the 99%,” say the banners and T-shirts, pointing out that 1% of the world’s population has somehow clawed its way to disproportionate money and power. Time to do something about this unnatural distribution, no?

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.

[Published on November 11, 2011]

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

Physicists and the financial markets – FT.com

Gene Stanley raises his fork, holds it out flat, a few inches above his plate of risotto. “The majority of traders still use Gaussian models and, when something outside the Gaussian happens, they have all these phrases, like ‘outliers’, but the main phrase is ‘shit happens’.”

He stares at his raised cutlery.

“Now, if we saw the forks start to levitate, it would be bizarre to say, ‘oh, shit happens’, but they do, that’s what they say. They say, ‘oh, you can’t predict everything’.”

With a chuckle, Stanley tucks back into his food.

The famous bell curve described by Carl Friedrich Gauss, the humble normal distribution that underlies so many statistical models, might explain most phenomena in a financial market but Stanley, professor of physics at Boston University, is interested in the levitating forks, the outliers, the “black swans” of Nassim Nicholas Taleb’s description.

Physicists and the financial markets – FT.com

Is another market crash around the corner? – Mark Hulbert – MarketWatch

Video: Is Another Market Crash Around the Corner?

A 1987-magnitude stock market crash could happen at any time.

Keep that in mind this week as commentators note the 26th anniversary of that crash, the worst in U.S. stock market history. If another crash of that magnitude were to occur today, the Dow would shed more than 3,400 in a single session.

Now consider this: Another crash that big is inevitable. No amount of government regulation can prevent it. You need to adjust your investment strategy accordingly.

That, at least, is the conclusion that emerges from academic research a decade ago into the frequency of market crashes. Xavier Gabaix, a finance professor at New York University and one of the co-authors of that research, told me earlier this week that their initial conclusion has been confirmed by numerous subsequent studies.

If the frequency of crashes of various magnitudes is so predictable, shouldn’t they be preventable?

Professor Gabaix says no. It’s their frequency that is predictable, not their timing.

Is another market crash around the corner? – Mark Hulbert – MarketWatch

A Theory of Large Fluctuations in Stock Market Activity

Xavier Gabaix, Parameswaran Gopikrishnan, Vasiliki Plerou, H. Eugene Stanley, MIT, Economics Department and NBER
Boston University, Physics Department, Center for Polymer Studies
August 16, 2003

Abstract
We propose a theory of large movements in stock market activity. Our theory is motivated by growing empirical evidence on the power-law tailed nature of distributions that characterize large movements of distinct variables describing stock market activity such as returns, volumes, number of trades, and order flow. Remarkably, the exponents that characterize these power laws are similar for different countries, for different types and sizes of markets, and for different market trends, suggesting that a generic theoretical basis may underlie these regularities. Our theory provides a unified way to understand the power-law tailed distributions of these variables, their apparently universal nature, and the precise values of exponents. It links large movements in market activity to the power-law distribution of the size of large financial institutions. The trades made by large financial institutions create large fluctuations in volume and returns. We show that optimal trading by such large institutions generate power-law tailed distributions for market variables with exponents that agree with those found in empirical data. Furthermore, our model also makes a large number of testable out-of-sample predictions.

A Theory of Large Fluctuations in Stock Market Activity

For more information about collapses see the following article: A System Collapse Framework for Societies | 1913 Intel

Photos: Yellowstone rebounds, 25 years after ‘tragic mistake’

Forests follow a power law distribution of collapses – fires. Put out the little fires and you get big fires. Put out all fires and you get Yellowstone 25 years ago – “the worst wildfire in Yellowstone history”.

Photos: Yellowstone rebounds, 25 years after ‘tragic mistake’

Twenty-five years ago, in a drought-parched and wildfire-swollen summer, 248 separate blazes charred 1.2 million acres in the greater Yellowstone area, while 50 fires inside Yellowstone National Park consumed more than a third of the park’s grounds. To date, it’s the worst wildfire in Yellowstone history.

Tuesday, Aug. 20, marks a quarter-century since Yellowstone’s worst single day, when, according to the National Park Service, winds increased the fire’s range by 150,000 acres.

This photo gallery includes more information from the Park Service’s “History of Wildland Fire in Yellowstone” and features scenes from a summer when fires in and near the park roared through more than a million acres over several weeks, shut down tourism and prompted government officials to reconsider their fire mitigation efforts. — Tim Skillern

Photos: Yellowstone rebounds, 25 years after ‘tragic mistake’

History of Wildland Fire in Yellowstone – Yellowstone National Park

The natural history of fire in the park includes large-scale conflagrations sweeping across the park’s vast volcanic plateaus, hot, wind-driven fires torching up the trunks to the crowns of the pine and fir trees at several hundred-year intervals.

Such wildfires occurred across much of the ecosystem in the 1700s. But that, of course, was prior to the arrival of European explorers, to the designation of the park, and the pattern established by its early caretakers to battle all blazes in the belief that fire suppression was good stewardship. Throughout much of the 20th century, park managers and visitors alike have continued to view fire as a destructive force, one to be mastered, or at least tempered to a tamer, more controlled entity. By the 1940s, ecologists recognized that fire was a primary agent of change in many ecosystems, including the arid mountainous western United States. In the 1950s and 1960s, national parks and forests began to experiment with controlled burns, and by the 1970s Yellowstone and other parks had instituted a natural fire management plan to allow the process of lightning-caused fire to continue influencing wildland succession.

The Fires of 1988

No one anticipated that 1988 would be radically different. In April and May, Yellowstone received higher-than normal rainfall. But by June, the greater Yellowstone area was experiencing a severe drought. Forest fuels grew progressively drier, and the early summer thunderstorms produced lightning without rain. The fire season began, but still without hint of the record season to come. Eleven of 20 early-season fires went out by themselves, and the rest were being monitored in accordance with the existing fire management plan.

The summer of 1988 turned out to be the driest in the park’s recorded history.

History of Wildland Fire in Yellowstone – Yellowstone National Park

Understanding Civil Unrest

Civil unrest

Professor Braha’s research, spanning a century of civil unrest in 170 countries, reveals that social instability is similar to various physical and biological phenomena, including earthquakes, forest fires and epidemics.

“Many biological systems are largely non-hierarchical and leaderless, too,” says biologist James Herbert-Read at Sweden’s Uppsala University. “This allows them to be robust to perturbations – take away a few individuals, whether they are cells, or individual animals, and the system still functions as a whole. Take away key nodes in hierarchical networks, and the system can fail. This makes non-hierarchical networks adaptable in the face of change.”

Stress

The dynamics of Professor Braha’s model are based on the hypothesis that widespread unrest arises from ongoing stress, outbursts of the stress and inciting communication among individuals through non-hierarchical social networks,” he says. “This leads to the spread of unrest across cities or urban areas that are connected through social and mass communication networks.”

According to his computer model and extensive collection of data, the shift to leaderless networks results from the fact that people have gradually become more interconnected beyond traditional hierarchies. This has led to a dramatic increase in civil unrest, similar to the thought experiment where influenza spreads faster in a more connected society.

His model also shows that accumulated stresses often lead to sudden spikes in unrest. “While the rates of social, economic and political stresses in particular regions are relatively stable, accumulating stresses during peaceful times leads to periodic outburst of unrest,” Professor Braha says.

Understanding Civil Unrest

Key point: What happens during the stable times is of utmost importance.