Currency Wars_ The Making of the Next Global Crisis - James Rickards [107]
Importantly, phase transitions can produce catastrophic effects from small causes—a single snowflake can cause a village to be destroyed by an avalanche. This is one secret behind so-called black swans. Nassim Nicholas Taleb popularized the term “black swan” in his book of the same name. In that book, Taleb rightly demolished the normal distribution—the bell curve—as a way of understanding risk. The problem is that he demolished one paradigm but did not produce another to replace it. Taleb expressed some disdain for mathematical modeling in general, preferring to take on the mantle of a philosopher. He dubbed all improbably catastrophic events “black swans,” as if to say, “Stuff happens,” and he left it at that. The term is widely used by analysts and policy makers who understand the “Stuff happens” part but don’t understand the critical state dynamics and complexity behind it. Yet it is possible to do better than throw up one’s hands.
A forest fire caused by lightning is a highly instructive example. Whether the fire destroys a single tree or a million acres, it is caused by a single bolt of lightning. Simple intuition might hold that large bolts cause large fires and small bolts cause small fires, but that is not true. The same bolt of lightning can cause no fire or a catastrophic fire depending on the critical state. This is one reason why black swans take us by surprise. They are called extreme events, but it would be more accurate to call them extreme results from everyday events. Extreme results will happen with some frequency; it is the everyday events that trigger them that we don’t see coming precisely because they are so mundane. Studying the system shows us how the everyday event morphs into the black swan. As in the case of the avalanche, what really matters is not the snowflake but the snow.
Two more concepts are needed to round out our understanding of complexity theory. The first involves the frequency of extreme events relative to mild events in a complex system, referred to as a degree distribution. The second is the concept of scale.
The bell-curve degree distribution used in financial economics says that mild events happen all the time and highly extreme events practically never. Yet the bell curve is only one kind of degree distribution; there are many others. The degree distribution that describes many events in complex systems is called a power law. A curve that corresponds to a power law is shown below as Figure 2.
FIGURE 2: A curve illustrating a power-law degree distribution
In this degree distribution, the frequency of events appears on the vertical axis and the severity of events appears on the horizontal axis. As in a bell curve, extreme events occur less frequently than mild events. This is why the curve slopes downward (less frequent events) as it moves off to the right (more extreme events). However, there are some crucial differences between the power law and the bell curve. For one thing, the bell curve (see Figure 1) is “fatter” in the region close to the vertical axis. This means that mild events happen more frequently in bell curve distributions and less frequently in power law distributions. Crucially, this power law curve never comes as close to the horizontal axis as the bell curve. The “tail” of the curve continues for a long distance to the right and remains separated from the horizontal axis. This is the famous “fat tail,” which in contrast with the tail on the bell curve does not appear to touch the horizontal axis. This means that extreme events happen more frequently in power law distributions.
Television and blogs are filled with discussions of fat tails, although the usage often seems more like cliché than technical understanding. What is even less understood is the role of scale. The curve shown above in Figure 2 ends at some point for convenience.