No really. This article that appeared in Wired and by Adam Mann details the study of chaotic systems and the uncanny affect of dragon king alignments presaging a crash or break down event. I am skeptical of the discussion concerning the ability to prevent and manage catastrophic events, as I am reminded of the law of unintended consequences, but having some advanced notice that a system is breaking down could be far more valuable.
Stop a stock trade and avoid a catastrophic global financial crash.
Seal a microscopic crack and prevent a rocket explosion. Push a button
to avert a citywide blackout.
Though such situations are mostly fantasies, a new analysis suggests
that certain types of extreme events occurring in complex systems –
known as dragon king events – can be predicted and prevented.
“A chaotic system may be in flux, and look like random behavior,” said physicist
Daniel Gauthier of Duke University, co-author of a paper appearing Oct. 30 in
Physical Review Letters. “But maybe there’s some internal structure we can identify that leads to destabilizing events.”
By looking at a simple experimental chaotic system, Gauthier and his
co-authors have been able to detect telltale signs that a dragon king
event was approaching and, most importantly, stop it from happening. If
this work can be generalized to more complex systems, such as climate,
power grids, and financial markets, it could be used to forecast and
perhaps forestall extreme behavior.
The story of this finding begins in the mid-90s when Gauthier was
studying the behavior of simple electronic circuits that were trained to
follow one another. His team did this by periodically measuring the
difference in either the voltage or current between the two circuits.
They would use this difference to give one system a tiny kick. The idea
was to synchronize the circuits as much as possible. And, for the most
part, it worked: One circuit followed the behavior of the other.
But occasionally, the two circuits would get out of whack.
Essentially, the leader circuit was losing control of its follower,
which would go off on its own and exhibit completely different behavior.
This desynchronization event would eventually get corrected – the tiny
kicks would push the follower circuit back to the same behavior as its
leader. But the results remained a bit of a head scratcher, until
Gauthier figured out what was going on.
A strange attractor first characterized by Edward Lorenz.
Image: Fractint/Wikimedia
Chaotic systems are often very simple. They can be characterized by
just a few parameters – in this case the voltage and current of the
circuit – but they also exhibit random and unpredictable behavior. Yet
the voltage and current of the system can’t take on just any value.
Instead, the parameters will stay within a somewhat narrow range. The
possible values within this range are what mathematicians call a
“strange attractor.” When plotted on an x and y axis, strange attractors
often take on odd shapes, sometimes looking like the wings of an
arithmetic butterfly.
The meeting points of these two wings – the “body” of the butterfly –
was where the desynchronization was happening in Gauthier’s circuits.
Imagine one circuit is traveling around on a wing of the butterfly,
pulling the follower circuit slightly behind it. From time to time, the
leader circuit would enter the meeting point of the wings and jump to
the opposite side. Usually, the follower circuit would come right along
with it but, every so often, the difference between them would be just
enough so that the follower circuit wouldn’t make the hop, instead
staying on the same wing.
“We would say that’s when they shred from each other,” said Gauthier.
“The two systems get ripped apart, basically going as far apart as they
can.”
And that was it. Gauthier studied these toy circuits, found an
interesting behavior, and explained it. At the time, it didn’t seem like
a big deal. But in the last few years, scientists in many fields have
been looking closely at the behavior of extreme events – very large
fluctuations in a system that often leads to catastrophic results. These
occur in many complex, chaotic systems: enormous
rogue waves in the ocean, extreme weather in the climate, or global stock market crashes.
One particular class of these extreme events is known as a
dragon king event.
This is a catastrophic occurrence that falls far outside a normal
expected probability. The name comes from looking at the wealth
distribution in a medieval society. If you plot the number of people who
have a particular amount of wealth, you would see many, many poor
farmers and a smaller number of wealthier landowners and noblemen.
Plotting the number of people versus a given amount of wealth would give
you a straight line.
Now the medieval king, who typically has an enormous amount of
wealth, would be outside this plot, far above the rest. Think of someone
like Bill Gates or Carlos Slim whose wealth dwarfs even that of a
modern one-percenter. While the rest of the population is described by
the simple line plot, these people are outliers.
So why dragon kings? Because, like dragons, certain extreme events
are entirely outside the normal classification scheme. “Dragons are
extraordinary animals of extraordinary properties,” said economist
Didier Sornette of the Swiss Federal Institute of Technology Zurich, another co-author of the work.
The
signature of a dragon king event, which is far above the normal
distribution and occurs far more often than other extreme events. Image:
Hugo LD de S Cavalcante et al, “Predictability and suppression of extreme events in a chaotic system”,
Physical Review Letters
Dragon king events may be freakish, but they are not freakishly rare. In fact they occur much more frequently than you would expect. Small
fluctuations in the stock market happen all the time and very large ones
rarely. But a dragon-king-type stock market drop would be one that was
both extremely large and occurred somewhat regularly. It would be like
seeing a once-in-a-century stock market crash every decade or so.
But stock markets are complex systems and hard to study. So Gauthier,
Sornette, and their collaborators looked at the difference between the
parameters of the two circuits in the leader-follower system. Very small
differences in the voltage or current were common, as expected. But the
extreme “shredding” events when the two circuits were very far apart
occurred much more often than would be expected from a normal
distribution. They had found one of the most pronounced dragon king
event signatures ever seen.
Even more interestingly, the researchers found that dragon king
events displayed characteristic signals announcing their approach (they
could only occur when the two circuits were on the “body” of the strange
attractor butterfly). Knowing that a dragon king was coming, they could
apply tiny perturbations to make sure the circuits stayed in sync. In
essence, they could forecast the arrival of a catastrophic event and
suppress it, prevent it from occurring.
By studying this simple circuit system, the scientists hope they
might be able to apply some lessons to more complex chaotic systems.
Economists, for instance, think some sort of rules might govern the
stock market (the rest of us aren’t so sure). If number crunchers could
uncover some of these rules and find the warning bells that are
correlated with crashes, perhaps they could also be avoided.
Of course, that’s been the dream of every trader since the London
Stock Exchange first opened up in a coffee shop in 1698. The question is
really whether or not the simple circuit-toy model can be applied to a
more complicated real-world system.
“That is where we’re really taking a leap,” said Gauthier.
The leader-follower circuits can be characterized entirely by a few
variables. Something like climate or the financial system is composed of
significantly more parameters, and no one really knows which ones might
be relevant or not.
In his work, Sornette has been working to identify what
might or might not be useful in predicting the behavior of the stock market.
His team keeps tabs on more than 20,000 assets worldwide to try and
diagnose bubbles. Using statistical analysis, they search for what he
called “trenchant super-exponential growth,” which is where the price of
an asset grows much faster than a simple compound interest. It is
possible that such behavior is a warning bell for financial bubbles.
“We are extremely active in the development of statistical methods to
apply to a major outstanding unsolved problem: the financial stability,
or instability, of the world,” he said. His research has looked at
possible ways to forecast changes in the financial market with some
encouraging results.
Being able to study dragon king events in an experimental system could be extremely useful, says physicist
Cristina Masoller
of the Polytechnic University of Catalonia in Spain, who studies
extreme events in complex systems but was not involved in the new study.
“Most of these events are in nature: precipitation, oceanic, or
economic systems,” she said. “The fact that they can be built in the lab
allows us to explore the origin of these events, and learn how to
generate and suppress them.”
But even if the research may one day help identify precursor signals
to dragon king events, there is no guarantee that they can be
controlled, added Masoller.
“Maybe the parameters that we need to control in order to avoid these
extreme events are a parameter we can not change,” she said.
Say that oceanic temperature is a relevant parameter in avoiding
catastrophic climate changes. Tuning such a variable up and down
precisely is likely to be out of human control. Even in something like a
financial system, the key parameter may be the amount of money each
individual in the world has. Changing something like that might be out
of the realm of possibility.
In complex systems “it’s possible the laws are simple, but maybe the
parameters we need to control are not very accessible,” she said.
Gauthier and Sornette are aware of the limitations of their
experimental model. But the point of the research was to “at least plant
the thought in people’s minds” that it might be possible to predict and
prevent dragon king events, said Gauthier. To make that happen,
however, scientists would probably
have to develop entirely new mathematical tools to identify the key variables in different complex systems, he adds.
