Connect, They Say, Only Connect

[Dave Monroe]

The New York Times
Saturday, January 25, 2003
Connect, They Say, Only Connect
By EMILY EAKIN

The whiteboard in Duncan J. Watts's office at Columbia
University was a thicket of squiggly blue lines,
circles and calculus equations. Mr. Watts, an
associate professor of sociology, had just begun a
passionate disquisition on the virtues and liabilities
of scale-free networks when the telephone rang. It was
Alfred Berkeley, the vice chairman of Nasdaq, hoping
to chat about the exchange's design.

Mr. Watts, 31, is a network theorist. And these days
that means fielding frequent calls from powerful
admirers like Mr. Berkeley — Wall Street moguls and
government officials eager to tap into a nascent
academic science that few understand but that many
think may hold the key to everything from predicting
fashion trends to preventing terrorism, stock market
meltdowns and the spread of HIV.

Never mind that Mr. Watts's new book on the subject,
"Six Degrees: The Science of a Connected Age," which
will be published by W. W. Norton next month, is
littered with the arcana of theoretical physics as
well as charts and graphs that appear to require an
advanced degree in math in order to decipher. Network
theory is hot. Two other recent books on networks,
"Linked: The New Science of Networks" (Perseus, 2002)
by Albert-Laszlo Barabasi and "Nexus: Small Worlds and
the Groundbreaking Science of Networks" (W. W. Norton)
by Mark Buchanan, have already sold tens of thousands
of copies.

And that's not counting sales in the burgeoning genre
of consumer studies, where network science terms and
concepts are invoked with near religious fervor....

[...]

Network scientists study networks: collections of
people or objects connected to each other in some way.
Think of the 1.5 million Manhattan residents or the
30,000 genes inside a human cell. Such networks,
scientists argue, behave in ways that can't be
understood solely in terms of their component parts.
Without knowing what every single person or object
within the network is doing, they say, it's
nevertheless possible to know something about how the
network as a whole behaves. 

[...]

Not that network theory is an entirely contemporary
creation. Its roots stretch back nearly 300 years, to
Leonhard Euler, a brilliant 18th-century Swiss
mathematician who dabbled in nearly every branch of
modern science, from algebra to astrophysics. In 1736,
Euler took up a brain teaser that had preoccupied the
residents of Königsberg, a Prussian town on the Pregel
River not far from where he lived: how to cross all
seven bridges in town without crossing the same bridge
twice. No one had been able to pull off the feat, but
Euler provided the mathematical proof that it could
not be done. To do so, he turned the problem into a
network, depicting the bridges as lines and the
landmasses they connected as nodes. 

After Euler, mathematicians continued to analyze
networks, then called graphs, enumerating the
properties of orderly and static structures like ice
crystals and beehives. No one thought to tackle
networks of people or objects that were, as Mr. Watts
puts it in his book, "actually doing something —
generating power, sending data or even making
decisions." Such complex real-world networks were
assumed to be random: nodes and links connected in an
arbitrary, disorderly fashion.

But clearly this is not always the case....

Of course, studying a network of six billion people is
an unfathomable proposition. It wasn't until the
mid-1990's and the advent of powerful computers that
network scientists were able to analyze real-life
networks of significant size and complexity. And in
doing so, Mr. Watts and his colleagues made some
tantalizing discoveries. By 1998, they had found that
networks as diverse as actors, power grids, the World
Wide Web, the proteins in a human cell and the neurons
of a wormlike organism called C. elegans aren't random
at all but obey the same simple, powerful rules.

For example, whether the network has nearly a billion
nodes (the estimated number of Web pages) or just half
a million (roughly the number of actors in the
Internet Movie Database), the paths between any two
nodes tend to be extremely short — such that, for
example, any two movie actors can be connected by an
average of less than four links.

That may not seem like news to anyone who has played
the Kevin Bacon Game ... or seen John Guare's play
"Six Degrees of Separation." ... But it was not
entirely clear why these should all be "small-world"
networks.... 

Eerier still, in 1999, Mr. Barabasi and a student at
Notre Dame found that many of these small-world
networks are also what scientists call scale-free.
Many natural phenomena, including traits like height
and I.Q., tend to cluster around an average (producing
the familiar bell curve distribution). By contrast,
scale-free networks go in for extremes: a few hubs —
nodes with lots of links — and many more nodes with
hardly any links at all.... 

Mr. Barabasi's discovery startled scientists. "People
always knew there were networks but thought they were
random," he said. "To know they were nodes linked by
hubs was very unexpected." 

It also provoked a frenzy of research. For as Mr.
Barabasi and his collaborator were able to show, the
structure of scale-free networks has important
practical implications. If you remove a few nodes at
random, the network can still function normally. But
if you remove one of the hubs, the results can be
catastrophic.

[...]

Yet just which network model describes human society
remains a subject of fierce debate....

[...]

"We like to think of our world as full of atomized
individuals," he said. "But decisions people make and
the actions they take are so hopelessly entwined with
the behaviors of everyone else that it's difficult to
draw the boundaries around the individual." .... 

But some scholars dismiss the network hypothesis
altogether....

[...] 

Mr. Watts admits that he faces daunting empirical
challenges — and that overzealous scientists are a
concern. "You can turn almost anything into a
network," he said, holding up two papers he had
received on the "small world of human language" and
shaking his head. "So what?"

"When I'm brutally honest with myself, I think that if
we can figure this out, we can answer some important
questions. Other times, I think it's just too hard."

http://www.nytimes.com/2003/01/25/arts/25WATT.html

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