Understanding the Small World Effect – Part II



Continuing with the previous post we look at some more interesting connections related to the Small Word Effect phenomenon and how could it really shape our planet’s future. There are many questions which come into minds of researchers and scientists all over the world. One such question was lodged in the mind of Duncan Watts, a 25-year old PhD student at Cornell University in New York. In 1995 while he was studying the mathematics of chirping crickets, and had run into a problem: how do chirping crickets fall into step so quickly? Was each one listening to all his fellow crickets, or just to his closest neighbours?

Then Watts recalled what his father had said about how everyone in the world is just six handshakes away from the President of the United States. Watts wondered if the same phenomenon could be linked to the speed with which the crickets began chirping in unison. Using an urban legend to solve a serious biological mystery is unconventional, to say the least, and Watts was nervous about suggesting the idea to his thesis advisor, mathematician Steven Strogatz. Yet Strogatz thought the idea was intriguing, and the two began to collaborate. In June 1998, they published a paper summing up their findings in the prestigious journal Nature – and in the process created a whole new science: The Small World Effect.

The Small World Effect can lead to a rumour spreading round the world with impressive speed. It starts by being passed around, say, an office in Canada, where it reaches the ear of someone with a friend in South America. If the rumour’s a good one, it can continue being passed on like this right round the world at double- quick time, as each of us is linked to everyone else by up to seven others.

For the first time, Watts and Strogatz demonstrated the power of a few random links to turn a sprawling world into a small one. Their success owed much to the ubiquity of computers. Unlike the theorists of the 1950s, Watts and Strogatz could call on computer power to create accurate simulations of the real world, with its close-knit communities and random links. They created an artificial ‘society’ of 1000 points, each one of which was connected to a clique of 10 ‘friends’. They found that if each clique consisted solely of nearest neighbours, then hundreds of steps were needed to get from one point to Watts and Strogatz had finally revealed how a planet of 6.7 billion people so often seems a small world.

While most of our friends may belong to our own little community, chance meetings have given us some who are randomly spread far more widely. And it is this handful of random links that short-circuits the vastness of the globe and turns it into a ‘small world’. Watts and Strogatz revealed the same effect at work in other ‘societies’. For example, using a computerised database of actors and their films, they showed that Hollywood is another ‘small world’. On average, any actor can be connected to any other via films involving just four intermediaries. Again, the reason is because of the links created by versatile actors like Rod Steiger, who worked in a huge if random range of films. Movie buffs had unwittingly exploited this for years when playing the so-called Kevin Bacon game, where an actor has to be linked to another via the fewest number of films. But if you connect an actor to Rod Steiger, things get much easier. The paper by Watts and Strogatz triggered huge interest in finding other real-life examples of the effect.

From the nervous system of worms to the network of computers making up the web, ‘small worlds’ have been found in many guises. The implications are often startling. For example, the Small World Effect keeps the internet operating, despite around three per cent of its crucial ‘router’ computers being down at any one instant, because of the presence of random links. But there’s a flip-side, as over 100 million people discovered in 2003 when key ‘nodes’ of several national power grids went down following apparently minor incidents.

The Small World Effect can turn a small local problem in a national power grid into one affecting millions – as was demonstrated several times in 2003. In August, sagging power-lines touching trees tripped circuit breakers that left 50 million people without power across eight US states, plus much of the eastern Canadian province of Ontario. The loss of power highlighted the existence of other ‘small worlds’ linked to the electrical grid, including Canada’s air and traffic networks, which were plunged into chaos. Later that same month, 500,000 Londoners in Britain were cut off by a single faulty transformer. And in September, storm damage to cables in Switzerland left the whole of Italy and parts of Switzerland without power for nine hours – leaving another 50 million people to ponder the power of the Small World Effect.

The rapid speed with which the world has been plunged into economic turmoil hints at the presence of the Small World Effect in big business. Mergers and tie-ups between companies in different sectors across the world have led to a complex network of links, creating a globalized, corporate Small World. And that means that if any part of it catches cold, the ‘short circuit’ effect can lead to the collapse of apparently utterly unrelated businesses with astonishing speed. Within days of the 9/11 attack in 2001, businesses ranging from local restaurants to national airlines had filed for bankruptcy. Within the last year, globalization of banks has recently allowed bad debts in the US to trigger collapsing profits in banks worldwide.

A similar effect is making itself clear in the financial world, where businesses that are apparently unconnected to the root cause of the recent turmoil within the business world are also suffering the effects. Major corporations have been shown to form a ‘small world’, with apparently unrelated companies being connected by relatively few links. This can help the business world ride out the storms that always affect a proportion of companies – but it can also spell trouble if a key corporation with more or less random links elsewhere runs into trouble.

The Small World Effect has proved especially important in understanding the spread of diseases. Scientists have traditionally focused on the infectivity of a disease to predict how epidemics spread. The Small World Effect shows that the nature of the society in which it breaks out can make all the difference. Studies published in 2001 by the Argentinian mathematician Damián Zanette suggest that if just 20 percent of the population has random links to people beyond the site of the first outbreak, a minor outbreak can turn into a major epidemic. Identifying such ‘superspreaders’ of disease – such as prostitutes in big cities or promiscuous tourists – can hold the key to stopping an epidemic in its tracks.

The same reasoning has prompted marketing experts to target influential opinion – formers from Oprah Winfrey to specialist bloggers in the belief that their vast networks of contacts can spark consumer interest in new products. But new research by Duncan Watts suggests that such ‘influentials’ aren’t as important as marketing experts think. Using computer simulations, he’s shown that pretty much anyone can spark a trend that spreads like wildfire – but only if people are ready for it. That may explain why, for example, some low-budget movies like the 2005 documentary March of the Penguins can become surprise hits while critically-acclaimed films like Ang Lee’s version of The Incredible Hulk flopped at the box office.

In other words, popularity doesn’t spread through a ‘small world’ like a disease. Understanding such subtleties is likely to reveal yet more surprises about the Small World Effect – and supply further proof that this ‘trivial’ social phenomenon is, in fact, anything but.


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