A brief recent history of webs - Complex Webs: Anticipating the Improbable - page 262

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A brief recent history of webs

Complex webs are not all complex in the same way; how the distribution in the num-
ber of connections on the Internet is formed by the conscious choices of individuals
must be very different in detail from the new connections made by the neurons in the
brain during learning, which in turn is very different mechanistically from biological
evolution. Therefore different complex webs can be categorized differently, each rep-
resentation emphasizing a different aspect of complexity. On the other hand, a specific
complex web may be categorized in a variety of ways, again depending on what aspect
of entanglement is being emphasized. For example, earthquakes are classified accord-
ing to the magnitude of displacement they produce, in terms of the Richter scale, giving
rise to an inverse power-law distribution in a continuous variable measuring the size of
local displacement, the Gutenberg-Richter law. Another way to categorize earthquake
data is in terms of whether quakes of a given magnitude occur within a given interval of
time, the Omori law, giving rise to an inverse power-law distribution in time. The latter
perspective, although also continuous, yields the statistics of the occurrence of indi-
vidual events. Consequently, we have probability densities of continuous variables and
those of discrete events, and which representation is selected depends on the purpose
of the investigator. An insurance adjustor might be interested in whether an earthquake
of magnitude 8.0 is likely to destroy a given building at a particular location while a
policy is still in effect. Insurance underwriting was, in fact, one of the initial uses of
probabilities and calculating the odds in gambling was another.
One of the first topics on the theory of probability was Abraham de Moivre's The
Doctrine of Chances , with the subtitle A Method of Calculating the Probability of the
Events of Play [ 14 ]. De Moivre was a Huguenot refugee from France who took shelter
in England and subsequently became a friend of Sir Isaac Newton. He was a brilliant
mathematician who managed to survive by tutoring mathematics, calculating annuities
and devising new games of chance for which he would calculate the odds of winning.
A mathematician could make a living devising new gambling games for the aristocracy
in the seventeenth century, if not by teaching them the secrets of the discipline [ 36 ].
Results from this 300-year-old treatise form the basis of much of what is popularly
understood today about probability and we have already used a number of his results in
the study of random walks. We mention these things to make you aware of the fact that
the uncertainty of outcome which is so obvious in gambling actually permeates our lives
no matter how we struggle to control the outcome of events. In this chapter we outline
one more calculus for quantifying and manipulating the uncertainty in the decisions we