麻豆传媒

Editorial: 鈥�Taming the beasts of the global economy鈥�

HUGO CAVALCANTE saw the disaster coming. From his lab at the Federal University of Para铆ba in Brazil, he detected the warning signs of an epic crash. At the last minute, he managed to nudge his system back to safety. Crisis averted.

OK, so Cavalcante鈥檚 impending crisis was only a pair of credit-card-sized circuits that were about to start oscillating out of sync 鈥� hardly the stuff of the evening news. But the experiment is the first to show that a class of extreme events, colourfully called dragon-kings, can be predicted and suppressed in a real, physical system. The feat suggests that some day we may also be able to predict, or in some cases prevent, some of the catastrophes in the real world that seem unstoppable, including financial crashes, brain seizures and storms.

鈥淧eople were hoping if you could forecast extreme events, maybe we could find a way to control them,鈥� says Cavalcante鈥檚 colleague at Duke University in Durham, North Carolina. 鈥淲e were able to completely suppress the dragon-king events.鈥�

Dragon-kings aren鈥檛 the first animal used to describe a class of catastrophic events. In 2001, Nassim Taleb published a book called The Black Swan, his name for catastrophes that always catch us off-guard. But though difficult to predict, black swans actually fall within an accepted mathematical distribution known as a exponentially more small events than large ones (see diagram).

Most events or objects found in a complex system 鈥� including earthquakes, hurricanes, moon craters, even power imbalances in war 鈥� also obey a power law, a ubiquity that some say hints at a deeper organising principle at work in the universe. Others, like Taleb, focus on the fact that a power law can鈥檛 predict when black swans will occur.

Now there鈥檚 another beast to reckon with. In 2009, Didier Sornette at the Swiss Federal Institute of Technology in Zurich some events lift their heads above the power law鈥檚 parapet, the way a king鈥檚 power and wealth vastly outstrip that of the more plentiful peasant. So big that they should be rare, these events have a greater probability of occurring than a power law would mandate.

鈥淭here seem to be certain extremes that happen much more often than they should if you just believe the power-law distribution predicted by their smaller siblings,鈥� Sornette says.

He christened them dragon-kings. The dragon part of the name stems from the fact that these events seem to obey different mathematical laws, just as a dragon鈥檚 behaviour differs from that of the other animals.

Sornette got his first whiff of dragon-kings when studying cracks that develop in spacecraft. Since then, he has , from a rainstorm that hit Venezuela in 1999 and the financial crashes in 2000 and 2007, to some epileptic seizures.

But he wasn鈥檛 satisfied with merely recognising dragon-kings. The fact that they don鈥檛 follow a power law suggests they are being produced by a different mechanism, which raises the possibility that, unlike events that follow the power law, dragon-kings may be predictable.

聯Catastrophic 鈥榙ragon-king鈥� events may be predictable as they form differently to standard events聰

He and his colleagues have had some success, predicting a slip in the Shanghai Stock Exchange before it happened in August 2009 and using a few electrical pulses to . But the difficulty of running controlled experiments in real financial systems or brains prevented them from going any further.

Enter Cavalcante and Gauthier鈥檚 oscillating circuits. Gauthier spent the early 1990s studying pairs of identical circuits that behaved chaotically on their own, but would synchronise for long periods of time when coupled in a certain way. 鈥淚t鈥檚 a little bit politically incorrect, but it鈥檚 sometimes called the 鈥榤aster-slave鈥� configuration,鈥� Gauthier says. He coupled the two circuits by measuring the difference between the voltages running through them, and injecting a current into the 鈥渟lave鈥� circuit to make it more like the 鈥渕aster鈥�. Most of the time this worked and the two would oscillate together like a pair of swinging pendulums, with only slight deviations away from synchronisation.

But every so often, the slave would stop following the master and march to its own beat for a short time, before getting back in step. Gauthier realised at the time that there were recognisable signs that this disconnect was about to happen. It wasn鈥檛 until he saw Sornette鈥檚 work that he checked for dragon-kings.

He and his colleagues have now shown that the differences in the circuits鈥� voltages during these desynchronisations are indeed dragon-kings. 鈥淭hey were as big as the system would physically allow, like a major disaster,鈥� Gauthier says.

The pair went on to show that they could reliably forecast when a big event was about to happen: whenever the differences between the circuits鈥� oscillations decreased to a certain value, a leap of dragon-king proportions was almost always imminent. And once they saw it coming, they found they could apply a small electrical nudge to the slave circuit to make sure it didn鈥檛 tear away from its master (Physical Review Letters, ).

鈥淲e basically kill the dragon-king in the egg,鈥� Sornette says. 鈥淭he counter-mechanism kills it when it is burgeoning.鈥�

聯We basically kill the dragon-king in the egg. The mechanism kills it when it is burgeoning聰

It鈥檚 a long way to go from a pair of coupled circuits to the massive complexity of the real world. But by using this simple system to find out at what stage in the process a dragon-king can be prevented, Sornette hopes to see whether financial regulation could prevent a crash once a stock market bubble has already begun to grow, a controversial topic among regulators.

鈥淭he fear of central banks is that their intervention might actually worsen the situation and trigger the crashes, destabilising the system even further,鈥� he says. 鈥淭hat鈥檚 the type of insight we could test and check and probe with our system.鈥�

Some physicists think the gap between so-called low dimensional systems like the pair of oscillators, which can be described by just three variables each, and real-world complex systems like the stock market, is too wide to bridge. 鈥淭he conclusions of the paper appear correct and interesting for people studying low dimensional chaos,鈥� says Alfred Hubler of the University of Illinois at Urbana-Champaign. 鈥淏ut in the real world, low dimensional chaos is very rare. Most real-world complex systems have many interacting parts.鈥�

Others agree with Sornette that having a simple physical system to manipulate will be useful. 鈥淗aving a mechanical system where you can explore it in the lab is crucially important,鈥� says Neil Johnson at the University of Miami in Coral Gables. He studies dragon-kings in simulations of stock markets and traffic jams and can鈥檛 wait to start using a pair of oscillators to see how they relate.

Sornette thinks the circuits are just the beginning of a future in which we can monitor, diagnose, forecast and ultimately control our world. 鈥淚 think we are on the verge of a revolution where we are going to be able to steer our planet better, informed by this kind of science.鈥� It鈥檚 quite a promise 鈥� not all storms, seizures and crashes are dragon-kings, after all. But we now have a tool to explore how to deal with those that are.

This article appeared in print under the headline 鈥淐rashing market, hidden dragon?鈥�