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6 - A brief recent history of webs

Published online by Cambridge University Press:  05 July 2014

Bruce J. West  and
Paolo Grigolini
Bruce J. West
Affiliation:
Army Research Office
Paolo Grigolini
Affiliation:
University of North Texas
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Summary

Complex webs are not all complex in the same way; how the distribution in the number 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 representation 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 according 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 individual 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.

Type
Chapter
Information
Complex Webs
Anticipating the Improbable
 , pp. 262 - 306
Publisher: Cambridge University Press
Print publication year: 2010

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