Bilfinger Berger Magazine 2/2009

A CHAIN OF JUST SIX PEOPLE SEPARATES EACH OF US FROM EVERY OTHER PERSON ON EARTH. AN EXERCISE IN “SMALL WORLD” THEORY.

The death of Marlon Brando had a particular effect on falafel vendor Salah ben Ghaly in Berlin. As a former art school student he had always admired Brando: “He played himself, and that is incredibly hard to do.” The Iraqi exile and the Hollywood movie star never actually met, but they came close. How? Through an experiment conducted by the weekly newspaper “Die Zeit.” The paper set out to show that the citizens of our planet are closer to one another than they realize, and chose the link between Ghaly and Marlon Brando as its example. The experiment aimed to prove a connection between them via a chain of just six friends and acquaintances. A time limit of a matter of weeks only served to heighten the suspense.

NETWORKS WORK TO RULES
The game had its origins in scientific theory. It was developmental psychologist Stanley Milgram who first drew attention to the “small world phenomenon.” His investigations of human networks in 1967 revealed that individual members of cliques and circles of friends had stronger connections to one another than outsiders (which was to be expected) and that the patterns of inhomogeneous networking in disparate groups are nevertheless similar (which was a big surprise).

Since the end of the 1990s, attention has once again been focusing on the “small world phenomenon.” Sociologist Duncan Watts and mathematician Steven Strogatz took a closer look at the structure of widely differing networks, armed this time—thirty years on from Milgram’s day—with powerful computer modeling systems. The objects of their investigations were the nervous system of the worm caenorhabditis elegans, the power station network in the western states of the USA and the connections between actors appearing together in the same films. They found that all three cases were examples of “small worlds.” Each node was connected with every other node via just a few switching stations. Also, rather than the connections being accidental, there were specific rules which produced similar patterns in all three networks. The two scientists were ecited: Had they stumbled on a generally applicable law that governs complex systems? It was also clearly apparent that their findings could have economic benefits, for example in improving the operating efficiency of a wide variety of networks.

FROM BERLIN TO BEVERLY HILLS
Meanwhile, however, their study inspired “Die Zeit” to attempt to prove the “six degrees of separation” between Berlin and Beverly Hills. Which could be the first link in the Marlon Brando chain? Falafel vendor Salah ben Ghaly suggested his friend Assad Al-Hashimi who lives in California. Here, ben Ghaly was unwittingly utilizing a particular property of networks: In addition to numerous short strands, they also feature a small number of long-distance links. The long link across the pond was successful: The friend jumped at the chance to join the project. As a Buddhist he actually sees a spiritual element in the idea that all human beings are networked: “I believe that all living creatures are linked to one another.” He (node 2) nominated a colleague he knows from his employer’s gym as the next in line (node 3). The colleague’s girlfriend Michelle (node 4) went to college with Christine Kutzer (node 5), who besides being a wife and mother is also the daughter of a big name in Hollywood. So as well as “normal people” she also has links to the stars—an ideal switch point in the Brando direction. Meanwhile, other journals had picked up on the search for the missing link. Newsweek and Time Magazine joined the fray.

Newspaper readers contributed the names of friends, acquaintances or colleagues who could extend the chain. An acquaintance of Christine Kutzer, Patrick Palmer who is a big player in the film business, looked to be the most promising candidate. He produced “Don Juan deMarco” with Marlon Brando. But did the two have contact with one another? His answering machine blocked progress. Palmer was away. And the clock was ticking.

The world is shrinking fast. If every individual knows a hundred other individuals (each of whom in turn knows a hundred others), then six intervening stages are indeed sufficient to network every individual on earth. Each of us will have had practical experience of the phenomenon. Let’s say we are far from home, on gorilla watch in Ruanda, and we meet someone from home. Immediately the search begins for common acquaintances—“Do you know so-and-so …?” Play the game long enough, and a connecting individual is bound to emerge. There is consolation here for those in fear of globalization: A web of friendships holds the planet in its embrace. A kind of Internet of emotional connections exists, and it existed long before modems were invented. It’s not fiber optics but feelings that span the globe.

ORDER PREVAILS
But this is not the reason why the “small world phenomenon” is the subject of intensive study. It was previously thought that networks were formed exclusively at random, provided only that the participants were free to create links at will. However, all of the networks investigated so far have established a specific order in a process of self-organization. A few nodes are connected by large numbers of strands, while most are linked by only a few. Remarkably, this pattern is evident irrespective whether we are talking of the network of airline routes or the web of citations that cross-reference one scientific publication with another. Some airports serve far more routes than others; some actors have appeared in many films and therefore are acquainted with more of their colleagues than, say, emerging new performers; some Internet servers handle far more data traffic than the rest. Ricard Solé, a biologist at the University of Barcelona, discovered when studying quite different biotopes (a lake, a forest, an estuary) that they exhibit striking similarities in the way they are networked. In any given ecosystem some types of animals and plants are far more interconnected than the rest and evidently function as key species. Solé is of the opinion that: “Nature evidently conforms to some universal principles of organization. If we can work these out, we may one day arrive at a general theory of complex systems.”

DIGITAL ECOSYSTEM
The way in which the Internet is growing is very much like an ecosystem. Users are, as it were, surrounded by a rampant jungle, with digital thickets and clearings, beaten tracks and data highways, open portals and branching routes. Anyone can plant another tree, and every planter is free to create a few paths through the thicket. There is no authority in the world that dictates how the more than 125 billion web sites may or may not be connected with one another via links and hypertext. And yet as in a real forest, the typical “small world” structure unfolds itself, with just a small number of sites and servers playing a key role. In cyberspace it takes a maximum of nineteen clicks to get from any one place to any other. The fact that more stages are required than in human networks is attributable to a simple reality: Internet sites have an average of only seven links, whereas it would be rather sad if each of us were in contact with only seven other people.

THE BENEFIT OF NETWORK GEOGRAPHY
The advantage of this self-organized inhomogeneous structure is that it reinforces the stability of the Internet. There is a high probability that when failures occur, one of the less important nodes is affected. The system as a whole doesn’t bat an eyelid. An ecosystem can cope with the extinction of individual plants and animals, the brain copes with the demise of an average of a thousand neurons per day. The Internet copes with local server crashes. The intrinsic robustness of the system can, however, only absorb faults and failures that affect one node or another at the whim of fate. It is a different matter when a network is subjected to a targeted attack. If an attacker knows the location of heavily interconnected switch points, the Achilles heels of the network, he or she can hit where it hurts. With increasing frequency, experts are warning that the feared attacks by crackers or cyber-terrorists on specific backbone servers could cripple the Web. Small world theory could help to identify the weak points, allowing us to come up with diversions and alternative routes.

Apart from security analyses such as these, there are other practical ways to use network geography:

// Search engines / Precise mapping of small worlds provides indications of “shortcuts,” for example as aids to orientation when searching through global data networks. The ambition is to make search engines so intelligent that they can direct users to the source of the information they seek with as few clicks as possible.

// Disease control / The interest of epidemiologists is focused on those individuals who have a particularly large circle of friends, acquaintances and colleagues and therefore make numerous contacts on a daily basis. They are the nodes by which infections may potentially spread particularly fast. As epidemics such as BSE and foot-and-mouth have shown, a combination of factors like “contagion” and “mobility” is especially dangerous.

// Marketing / It has been shown in the USA that word-ofmouth recommendation is one of the most important channels through which a book achieves prominence and even bestseller status. Once again the task here is to find the readers who are most highly networked and wow them!

// Nature conservation / In the small worlds of ecosystems, some species play a key role. Many other species are dependent on them. On the other hand, these are generally not as one might perhaps expect the large, charismatic creatures, favorites of the public such as lions, elephants or gorillas, but small, inconspicuous species. Krill for example are a mainstay of maritime ecosystems: Without krill there would be no whales, seals, penguins. Given the threat to natural habitats and the chronic shortage of funds, small world analyses could help to concentrate conservation efforts on key species.

Networks make the world smaller, but only for those who are networked. The distance between two points shrinks as soon as they become connected, whether by a road, a telephone line or a bond of friendship. For all those who are not connected, there is an inverse change in geography. The more participants there are gathered together in a network, the greater the isolation and the disadvantages suffered by those who are left outside. If there were only ten fax machines in Germany, it wouldn’t matter if I didn’t have one. But with ten million, it is a different matter. There is an expectation that I should be connected. This explains the strong pull that networks exert. They shrink time and space. The issue divides culture-pessimists and cyber-utopians. The first are afraid that through networking they will constantly be confronted with what is foreign, strange and imponderable. The second are working on a radical redefinition of closeness that is no longer measured by physical proximity but by emotional affinity. The former suffer from anxiety overload, for the latter Marlon Brando is a fellow-citizen who lives just six friends away in Los Angeles.

AN ANSWER AT LAST
Node no. 6 still had to be found. For weeks Patrick Palmer, the missing link in the chain from falafel vendor to film star, did not return the calls. The readers were becoming as nervous as the editors. A women’s magazine suggested, forget Brando, how about Brad Pitt? A whole series of new chains were proposed. One of them that would have been routed via an attorney in the film industry was tested, but it ended in a blind alley. Fortunately the six degrees of separation rule states only that any two inhabitants of the earth are no more than six acquaintances removed from one another—not how long it takes to find these six. Weeks later Palmer phoned back. Yes, he had produced “Don Juan deMarco” with Brando, they met sporadically, Brando lived not far away. OK, he would try to call him.

The connection between the Iraqi falafel vendor and the American film star was made. Nevertheless the two never met. But the world had edged a fraction closer together.

(By Michael Gleich, Illustration: Silke Beneke)
Bilfinger Berger Magazine 2/2009