One of the founding principles of traditional economic theory, is that
when making economic decisions, we are independent. Like self-contained
atoms in a gas, we only interact by bumping up against each other in the
marketplace.

In the 19th century, neoclassical economists such
as William Stanley Jevons and Léon Walras were directly inspired by the
atomic theory of physics. Individuals or firms were equated with atoms.

Later,
economists would compare the apparent random walk of the marketplace
with the so-called Brownian motion of tiny particles of dust or pollen
as they are buffeted around by colliding atoms. The ultimate realisation
of this atomic vision of the economy was Eugene Fama’s efficient market
hypothesis, which asserted that the actions of independent investors
would drive prices to their optimal level.

Today, risk models
used by companies and banks implicitly assume that economic decisions
are taken independently. In economic terms, we are still in the age of
the atom. But thanks to input from other areas of science – including
physics – that is beginning to change. Economics is entering the age of
the network.

It has long been known by physicists that atoms or
molecules are capable of organising themselves into connected networks,
with a dramatic effect on the material’s properties. For example, when
water freezes, large clusters of molecules spontaneously align
themselves into the highly ordered network known as ice.

In the
late 1950s, mathematicians gained insight into such phase changes
through their study of randomly connected networks. As connections are
randomly added to a large enough collection of nodes, at first most of
the connected groups will only consist of two individuals. As more
connections are added, larger clusters slowly begin to form. And at a
certain threshold the group suddenly gels into a cohesive whole, like
water freezing.

Random networks have the advantage of being
mathematically tractable, but they are a rather coarse model of society,
which – being made up of people instead of atoms or molecules – is not
like the random disorder of a gas, or the pure order of a solid, but
shows a richer and more complex structure.

This was illustrated
in the 1960s by Harvard psychologist Stanley Milgram, who performed
experiments in which he mailed out a number of letters to randomly
selected people in the US. Each letter gave information about a target
person, and asked the recipient to forward the letter to a personal
acquaintance who they thought would be likely to know that person.
Milgram was amazed to find that, although some letters never made it to
their destination, others did in just a couple of mailings, and the
median number of mailings was only six.

Thus was born the idea
of “six degrees of separation.” This became the title for a 1990 play by
John Guare, the title of the film adaptation, and eventually a cliché.

Attractive
as the “six degrees” notion is – it’s nice to think that we’re all part
of one big family – scientists have since questioned its accuracy. In
Milgram’s experiments, less than 30 percent of the letters reached their
destination, and the rest were omitted from the results. As psychology
professor Judith S. Kleinfeld wrote, the empirical evidence suggests
that the world is not uniformly connected, but more “like a bowl of
lumpy oatmeal,” with some of us well-connected, and others much less so.

While
it may be debatable to say that human society is what scientists call a
small world network, it is certainly getting smaller all the time – at
least for some things. The rapid spread of diseases such as SARS or the
recent swine flu is evidence of that. The existence of fast transport
links between countries means that diseases can spread around the world
in a couple of days.

So what relevance does this have for the
economy? Well, network scientists have recently shifted their attention
to studying financial networks – and their findings are in some respects
alarming. In recent decades, the world financial system has become
increasingly connected.

The figures below, from a Bank of
England report, show the cross-border stocks of external assets and
liabilities in 18 countries, in the years 1985 and 2005. Node size is
proportional to total external financial stocks, and the thickness of
the links is proportional to bilateral external financial stocks
relative to GDP.

Over those two decades, the node sizes have
increased by about a factor 14, and links by a factor six. As the
report’s author Andrew Haldane notes, “The network has become markedly
more dense and complex. And what is true between countries is also
likely to have been true between institutions within countries.”

Instead
of six degrees of separation, the average path length between larger
countries is now more like 1.4. This isn’t a small world – it’s a
crowded bar. Information propagates rapidly, but – as shown by the
recent crisis – so do problems. If anyone gets a cold, everyone gets it;
and a credit freeze can turn the entire network to ice. Robust
networks, such as those found in healthy ecosystems, tend to be built up
from smaller, weakly-connected subnetworks.

A first step
towards making the financial system more robust is therefore to
introduce a degree of modularity. Some ideas being floated include:
separating investment banks from commercial operations; breaking up the
largest institutions along regional lines; or introducing a Tobin tax
(or variant thereof) on financial transactions that would slow the
global flow of money.

These might make the system less efficient
in the short term, but they should also make it more robust. After all,
when it comes to deadly viruses or credit crises, “It’s a small world,
isn’t it?” is the last cliché you want to hear.