De Econometrist neemt een statistische kijk op de wereld.

**In 1994, four Albright college students created a game called “The six degrees of Kevin Bacon”. This game’s aim is to connect any actor in the Hollywood scene with the actor Kevin Bacon, using at most 5 actors with who they have worked (in)directly. The students came up with the idea after Kevin Bacon stated in an interview with Premiere magazine that “he had worked with everybody in Hollywood or someone who’s worked with them.” **

**After the young students and Bacon were invited to a TV-show to explain their game, its popularity increased substantially. Even a board game based on the concept was released and the “Bacon number” was invented. This number is the degrees of separation between an actor and Kevin Bacon. This new game implied some great success for Kevin Bacon, even though the concept of the game was not new at all.**

The six degrees of separation is the idea that all people are connected with each other by at most six social connections. The concept is often referred to as “The Six Handshakes Rule” and was originally set out by Frigyes Karinthy in 1929. Theories based on the idea were already discussed after World War I, but it was Karinthy who published a bundle of short stories including a piece called the “Chain-Links”. In this story, he particularly tells that he believed that the modern world was ‘shrinking’ due to this ever-increasing connectedness of human beings. As a result of this hypothesis, characters in the tale believed that any two individuals could be connected through at most five acquaintances.

Karinthy’s notion on the six degrees of separation led to a lot of interest under, of course, psychologists and in cultural projects. American playwright John Guare wrote a play in 1990 and released a 1993 film that popularized it. The play appropriately contemplates about the idea that any two individuals are connected by at most five others.

The Kevin Bacon game was preceded by the John L. Sullivan game, in which people would ask others to “shake the hand that shook the hand that shook the hand that shook the hand of ‘the great John L.’’’

Furthermore, the concept has been remarkably often used in different forms of entertainment. Multiple songs and more than ten television shows were based on the six degrees of separation. One of those shows was the weekly section *Dossier Costers* on the production *Man Bijt Hond*, in which a worldwide event from the past week would be linked to Gustaaf Costers, an ordinary Flemish citizen, in six steps.

Various films were also based on the concept, like the Oscar-winning film *Babel*. In this film the lives of all of the characters were intimately intertwined, although they did not know each other and lived thousands of miles from each other.

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It can obviously be concluded that the “small world” phenomenon made its way through entertainment, but has the theory even been proven? Several studies have been conducted to test the concept. One of those studies is the Milgram’s small world experiment, where the degree was tested across the US population. In 1973, Milgram used simulations on quite limited computers and predicted that there existed approximately three degrees of separation between US citizens. However, his experiment was scaled, which certainly differs from testing it globally. It also does not include isolated groups of people, like native Brazilian populations. These groups could possibly not have any contact whatsoever with the rest of the world. Hence the “six degrees” claim is often said to be an “academic urban myth”.

Luckily, the rise of social media in the past decades, and thus connectivity, could possibly deliver a prove for the phenomenon. For both Facebook and Twitter, researchers produced promising outcomes. In 2011 Facebook’s data team released two papers that stated that amongst all Facebook users at the time of research, there is an average distance of 4.74. Probabilistic algorithms were applied to statistical metadata to verify the accuracy of the measurements. It was also found that 99.91% of Facebook users were interconnected, forming a large connected component. Comparably, social media monitoring firm Sysomos stated that users on Twitter are approximately connected by a distance of 4.67.

Furthermore, LinkedIn is actually partially based on the concept, as one’s network is made up of first degree, second degree, and third degree connections and fellow members of LinkedIn Groups. In addition, LinkedIn notifies the user how many connections they and any other user have in common

Mathematicians also tried to approach the idea in a mathematical way: the people we want to connect can be seen as nodes and their connections as edges. Then, by the six degrees of separation, it should hold that the maximum length of a path between two nodes is six.

In the easier case for the Bacon Number one could use a shortest path algorithm, as the set of nodes is limited to the number of actors in Hollywood. This network would still be extremely large, but far more manageable than a network including the entire world population.

To prove the complete concept, one would have to construct an arbitrary proof for every pair of nodes. Watts and Strogatz showed that the average path length between two nodes in a random network is equal to

*Degrees of Separation* = ln *N* / ln *K,*

where *N* is equal to total nodes and *K* is the acquaintances per node. Thus if *N* = 7,000,000,000 and *K* = 45 then *Degrees of Separation* = 22.67 / 3.81 = 5.96.

The mathematical solution seems to give a rather reliable outcome. However, there are still some important differences between using mathematics and the real world. For example, one cannot simply assume that the average person has 45 acquaintances and, as said earlier, population groups separated from the rest of the world are not taken into account.

Proven or not, the six degrees of freedom is a concept that is popular in various fields and will certainly be investigated in the future. With our ever-improving technology and the aid of social media the six handshakes rule in the future maybe will no longer be a phenomenon but a fact. Until then, I might try and achieve some success with a new simple game I created, the Casper de Vries Game…

This article was written by *Casper de Vries*