Webs - Complex Webs: Anticipating the Improbable - page 1

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Webs

The science of complex webs, also known as network science, is an exciting area of
contemporary research, overarching the traditional scientific disciplines of biology,
economics, physics, sociology and the other compartments of knowledge found in
any college catalog. The transportation grids of planes, highways and railroads, the
economic meshes of global finance and stock markets, the social webs of terrorism,
governments, and businesses as well as churches, mosques, and synagogs, the physical
lattices of telephones, the Internet, earthquakes, and global warming, in addition to the
biological networks of gene regulation, the human body, clusters of neurons and food
webs, share a number of apparently universal properties as the webs become increas-
ingly complex. This conclusion is shared by the recent report Network Science [ 23 ]
published under the auspices of the National Academy of Science. The terms networks
and network science have become popular tags for these various areas of investigation,
but we prefer the image of a web rather than the abstraction of a network, so we use
the term web more often than the synonyms network, mesh, net, lattice, grille or fret.
Colloquially, the term web entails the notion of entanglement that the name network
does not share. Perhaps it is just the idea of the spider ensnaring its prey that appeals to
our darker sides.
Whatever the intellectual material is called, this topic is not about the research that
has been done to understand complex webs, at least not in the sense of a monograph.
We have attempted to put selected portions of that research into a pedagogic and often
informal context, one that highlights the limitations of the more traditional descriptions
of these areas. In this regard we are obligated to discuss the state of the art regarding a
broad sweep of complex phenomena from a variety of academic disciplines. Sometimes
properly setting the stage requires a historical approach and other times the historical
view is replaced with personal perspectives, but with either approach we do not leave the
reader alone to make sense of what can be difficult material. So we begin by illuminating
the basic assumptions that often go unexamined in science.

1.1 The myth of normalcy

Natural philosophers metamorphosed into modern scientists in part by developing a
passion for the quantifiable. But this belief in the virtue of numbers did not come about
easily. In the time of Galileo Galilei (1564-1642), who was followed on his death by