Webs - Complex Webs: Anticipating the Improbable - page 39

predictable in that those events which are the most influential are the most difficult
to predict. The complexity of these webs is manifest through the domination of the
phenomena by the extreme values of the dynamics. Taleb calls this the Black Swan [ 32 ]
because it is the deviant, the black swan, that ultimately determines the outcome of an
experiment, not the average behavior. Recall our discussion of the citations of scientific
articles; the average number of citations cannot be used to characterize the citation
process because of its inverse power-law form. The black swan is unpredictable and
yet its existence very often determines what can and cannot be known about a complex
web.
Perhaps an example will serve to clarify this point. The black swan was set in an eco-
nomic context and requires a certain amount of background to understand the influence
of extrema, but there is another, more direct phenomenon with which we are familiar; a
blackout. Hines [ 15 ] defines a blackout as being any power-network event that results in
an involuntary interruption of power to customers and lasts longer than 5 minutes. When
the power grid fails its influence is geographically dispersed, potentially affecting liter-
ally millions of people and crippling entire regions of the country. The data available
from the North American Electrical Reliability Council (NERC) for 1984-2006 indi-
cate that the frequency of blackouts follows an inverse power law and the frequency of
large blackouts in the United States is not decreasing, in spite of the safety measures put
into place to mitigate such failure over that time period; see, for example, Figure 1.14 .
Part of what makes this example so interesting is that, in order to allocate resources
and anticipate the event's effect, policy makers must know the patterns that appear in
the data, namely the relationship between the size of an event (a blackout in terms

The cumulative probability distributions of blackout sizes for events greater than S in MW. The
crosses are the raw data; the solid line segments show the inverse power-law fits to the data and
the dashed curve is the fit to the Weibull distribution. Reproduced from [ 15 ] with permission.

Figure 1.14.