SO MANY parties, so little time 鈥� so how to choose which one to grace with your presence? Time was when there was no option but to line up the invitation cards and pick the most promising. But that鈥檚 all in the past, thanks to mobile phones. Now you can find out what all those parties are like by calling friends on the spot and comparing notes. After a few phone calls, the jury is in and it鈥檚 time to head for the Best Party in Town.
It sounds like the perfect solution to the party problem. But according to two German physicists it is a recipe for disaster. In a paper about to appear in the International Journal of Modern Physics, Steffen Trimper and Marian Brandau of the Martin Luther University in Halle, Germany, show that mobile phones can ruin everybody鈥檚 evening.
Just ask Tobi. His little party in Berlin was going just fine until some early arrivals rang to tell their friends what a fab time they were having. The result was like a 鈥渘uclear chain reaction鈥�, Tobi later told the German magazine Der Spiegel. Hordes of people from all over Berlin responded to the calls, and called their friends as well, before heading straight for Tobi鈥檚 flat. In the end, what had been a quiet gathering became a full-on frenzy of 120 people. 鈥淚t was barely possible to control it,鈥� Tobi said. 鈥淭he police came round three times.鈥�
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It was Tobi鈥檚 story that first got Trimper thinking about the way parties can go wrong. 鈥淎fter reading the article, I spoke to my sister, and found that her daughters had seen this phenomenon,鈥� Trimper recalls. 鈥淎nd so had my PhD student.鈥� It seemed there was some genuine phenomenon at work.
And it was an intriguing one. To Trimper, who spends his time pondering the actions of molecules in solids, the descriptions of how parties suddenly take off sounded like a 鈥減hase change鈥�, such as when ice turns to water. Brandau, meanwhile, saw hints of 鈥渟ocial network鈥� effects which arise from the way apparent strangers often have unexpected friend-of-a-friend links. Were these parallels a coincidence, or could the actions of party-goers be captured by some bizarre combination of solid state physics and network theory? Trimper and Brandau decided to investigate.
They began by constructing a mathematical model whose origins lie in a now famous experiment conducted almost 40 years ago by the American sociologist Stanley Milgram. He sent letters to around 300 randomly chosen people in the US, explaining that the letters were to be forwarded on to a target person in Massachusetts. Which sounds simple enough, except that the recipients weren鈥檛 told the address of the target: only his name, occupation and a few other personal details. They were asked to send the letter to any acquaintance they thought had a better chance of knowing the target. Milgram made a note of how many re-postings were needed before the letters reached their target.
Unsurprisingly, most of the letters never arrived. But 20 per cent did 鈥� and, astonishingly, usually after passing between just five or six intermediaries. Milgram鈥檚 discovery confirmed the suspicions of countless party-goers who find mutual friends in common: it really is a 鈥渟mall world鈥�.
Network theorists have discovered that it only takes a sprinkling of random long-range links to short-circuit an otherwise sprawling network and turn it into a small world where everyone is connected to everyone else via just a few intermediaries. But of course that doesn鈥檛 explain how people home in on this handful of long-range links so effectively. After all, we may know some of our friends鈥� friends, and even some friends of theirs, but the resulting circle of acquaintances is hardly vast.
鈥淭his has implications beyond the party scene, such as getting new products to market鈥�
This part of the mystery was resolved in 2002 by a team led by sociologist Duncan Watts at Columbia University in New York. The team pointed out something the mathematicians had overlooked (some might say all too predictably): people aren鈥檛 just points on a network. We all have a host of different facets to our character, from nationality and gender to occupations and interests. As such, the notion of the 鈥渓ength鈥� of social links is far richer than mere geographical distance: people can be separated by continents, yet still have much in common. Faced with choosing the next recipient of a letter in Milgram-style experiments, people tend to pick friends with two or three traits in common with the target. And Watts and his colleagues showed that this gives far more scope for hitting those crucial random long-range links that turn big networks into small worlds.
Picky people
But they also found that another factor plays a key role: clannishness. If we were all very picky about the company we keep 鈥� or highly 鈥渉omophilic鈥� in the argot of social network theory 鈥� the world would be made up of isolated cliques with nothing to say to each another. If, on the other hand, we found one another endlessly fascinating regardless of background, the world would be one big babel.
The real world is clearly somewhere in between, and Watts and his colleagues showed the small-world effect can survive a certain amount of clannishness. For parties, however, Trimper and Brandau have discovered that the same effect can spell disaster.
In trying to understand the runaway party effect, Trimper and Brandau incorporated the theory developed by Watts and his colleagues into a computer simulation. They created a virtual community of 1000 party-goers, whose overall level of homophilia the researchers could vary from risibly snooty to wantonly promiscuous. They set the homophilia level, gave all the party-goers virtual mobile phones and packed them off to 10 virtual parties. Once at their party, each would report back to their friends elsewhere. 鈥淲e kept things very simple,鈥� says Trimper. 鈥淭he idea was to see how many friends they knew at the party, and if they heard of a party with more of their friends, they would leave and go to that one.鈥�
With only one variable to control 鈥� the level of homophilia 鈥� the model was certainly simple. Yet Trimper and Brandau found that once the homophilia reached a critical level, the guests would suddenly start reaching for their virtual coats. They became so picky about who they spent time with that they quit parties with too few like-minded people and ended up at one party with all their snooty friends. When that happened, all but one of the virtual hosts was left weeping over their canap茅s.
The real surprise is that all this happens at a critical level of pickiness. 鈥淭he effect was very sudden, like a phase change,鈥� says Trimper. 鈥淲e had no expectation that so simple a model would give rise to something like this.鈥� Even so, the pair are convinced the model鈥檚 behaviour reflects a genuine effect, and one with implications far beyond the party scene. For example, it may cast light on how new ideas come to dominate the thinking of particular groups, such as political factions. It also suggests ways of getting new products to dominate the market by exploiting word-of-mouth recommendations.
The key lies in the homophilia level, which is somehow related to how many short and long links there are in people鈥檚 social networks. The exact nature of that relationship is still unclear; Trimper is working overtime to get to grips with all the implications of the findings. But, he points out, one implication is already clear. 鈥淲hen your party guests arrive,鈥� Trimper says, 鈥渕ake sure you take their mobile phones as well as their coats.鈥�
