What is the theory of six handshakes and what does mathematics have to do with it?

In a world of over eight billion people, is it possible to trace a social connection between any two random people in just «six handshakes»? An international team of mathematicians tested this acclaimed theory and the results were astonishing. Hollywood actor Kevin Bacon, the unofficial spokesman for this unusual social concept, may be just as surprised: experts have confirmed that it actually takes an average of six handshakes to establish a connection between any two people. Yes, yes, in a game called «six steps to Kevin Bacon» (eng. Six Degrees of Kevin Bacon), participants must, in no more than 6 transitions, find a connection between any actor and Kevin Bacon through the actors with whom they starred. And there really was a connection. Let's figure out what kind of theory this is and what relation actors and exact sciences have to it.

What is the theory of six handshakes and what does mathematics have to do with it? The theory of six handshakes has been confirmed by mathematicians. Image: blog.fyself.com. Photo.

The theory of six handshakes has been confirmed by mathematicians. Image: blog.fyself.com

Six Handshakes Theoryis a sociological theory that states that any two people on Earth are separated by no more than five levels of mutual acquaintances.

Contents

  • 1 Origins of the theory
  • 2 Social connections
  • 3 Six steps to Kevin Bacon
  • 4 Mathematical proofs of the theory of six handshakes

Origins of the theory

The theory of six handshakes dates back to 1967, when Professor Stanley Milgram of Harvard University conducted an innovative experiment by sending 300 identical letters with similar instructions across the United States. Letters had to pass through certain social circles until they reached the specified addressee.

The experiment revealed a striking pattern: the paths that crossed and connected people in different parts of American society were surprisingly short:letters reached to the addressee in about six exchanges.

The origins of the theory. Social connections between people have a certain pattern. Image: stephenornes.com. Photo.

Social connections between people have a certain pattern. Image: stephenornes.com

In the decades since the experiment was conducted, numerous studies have been conducted on the theory of six handshakes, or “six degrees of separation,” on topics ranging from interactions with actors to friendships in social networks, gave the same results, showing that the average number of handshakes connecting any two peopleequals six.

More on the topic: Scientists have proven the theory of six handshakes and found that there are fewer people in the chain

But the pressing question remained open: why six? The answer finally came in a paper published in the journal Physical Review X. The study's authors include researchers from Israel, Spain, Italy, Russia, Slovenia and Chile.

Social connections

In the study, the team examined the dynamic equilibrium of human behavior in which the tension between the desire for social prominence and the associated costs of forming and maintaining social connections arises.

People naturally gravitate towards central roles in social networks, carefully choosing associations that propel them into these positions. However, any new relationship requires an investment of time and energy, which leaves a tangible imprint on each connection, the authors of the work explain.

Social connections. Any person on Earth is connected to someone else by a chain of acquaintances no more than six people long. Image: cff2.earth.com. Photo.

Any person on Earth is connected to someone else by a chain of acquaintances no more than six people long. Image: cff2.earth.com

The research paints a picture of a network filled with nodes, or “rational agents,” who constantly evaluate the costs and benefits of their relationships with others. Each agent in this networked world is in a state of constant evaluation, that is, constantly weighing everything «for» and «against» creating new connections and maintaining existing ones – and all this in an effort to strengthen your own influence.

Read even more interesting articles about the latest discoveries in the field of science and high technology on our channel in Yandex.Zen – articles are regularly published there which are not on the site!

The results of the study show that social networks are a dynamic hive of people constantly playing the cost-benefit game, breaking ties on the one hand and establishing new ones on the other. «This is a constant excitement caused by the desire to take a central place in society. Ultimately, when this tug-of-war reaches equilibrium, all people receive their position in the network, a position that best balances their desire for fame and limited budget for new acquaintances, says the official press release of the work.

Social connections. It’s amazing, but in this huge world we are connected to each other by mutual acquaintances. Image: mir-s3-cdn-cf.behance.net. Photo.

It’s amazing, but in this huge world we are connected to each other by common acquaintances. Image: mir-s3-cdn-cf.behance.net

Having carried out mathematical calculations, the authors of the article discovered an amazing result: this process always ends in social wayscentered around the number sixwhich in itself is quite surprising. It is also necessary to understand that each network participant acts independently, without any knowledge of a given theory or intention. And yet, this independent game forms the structure of the entire chain, which means we are dealing with the phenomenon of a repeating pattern of six steps (or six steps).

This is interesting: The science of friendship: how we gain and lose friends

Six steps to Kevin Bacon

Without knowing it, Hollywood actor Kevin Bacon made a significant contribution to the science and theory of six handshakes. It all started with an interview with Premiere magazine in 1994, in which Bacon noted that the actors with whom he starred in the film Wild River worked with all of his Hollywood colleagues. This initially little-known fact formed the basis of a game played by three students who, during parties, discussed the number of films in which the actor has starred and how many other actors he knows.

The students asked people to tell them the actors' names and looked for their connection to Bacon. As a result, the guys gained fame, took part in evening TV shows and then, together with Kevin Bacon, wrote a book called “Six Degrees of Kevin Bacon” («Six Steps to Kevin Bacon»). Later, Endless Games released a board game based on it.

Six steps to Kevin Bacon. Kevin Bacon is the center of the Hollywood Universe. Image: upload.wikimedia.org. Photo.

Kevin Bacon is the center of the Hollywood Universe. Image: upload.wikimedia.org

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Mathematical proof of the theory of six handshakes

It is also interesting that the theory of six handshakes (and “six steps to Kevin Bacon”) has a mathematical basis and numerous studies. One such example is Milgram's “small world” experiment, in which in 1973 the scientist used simulations on a fairly limited number of computers and predicted that there were approximately three handshakes between US citizens.

Milgram's experiment has its limitations, of course, but the rise of social media in recent decades, and therefore Internet connectivity, provides evidence of this phenomenon – researchers have found promising results by studying people's connections on Facebook and X (formerly Twitter). In 2011, Facebook's data team published two papers stating that 99.91% of Facebook users are connected to each other, and their connection forms a kind of chain.

Mathematical proof of the theory of six handshakes. Modeling allows you to analyze the properties of connections between people and describe how the structures of real social connections are built. Image: i.ytimg.com. Photo.

Modeling allows you to analyze the properties of connections between people and describe how the structures of real social connections are built. Image: i.ytimg.com

Mathematicians have also tried to approach this idea from a scientific point of view: the people we want to meet can be considered as nodes, and their connections as a chain. Then, given the theory of six handshakes, we should assume that the maximum path length between two nodes is six. The math solution seems to produce a fairly reliable result.

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However, there are some important differences between using math and actually peace. For example, you can't just assume that the average person has 45 acquaintances, and there are groups separate from the rest of the world that are not taken into account. One way or another, the theory of six handshakes is quite popular and will become the object of scientific research more than once in the future. In the meantime, we can draw the following conclusion – the world is, after all, a small place.


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