To be honest, not particularly, I believe in all this, but there is such a theory.
For the first time, the idea that any two people in the world can be connected by a sequence of personal contacts and that this chain in most cases will be composed of a certain number (namely, five) links, was formulated by the Hungarian writer Frieds Carinthi. His story, written in 1929, was called "The Links of a Chain". The story was about a kind of game, a thought experiment aimed at proving that the population of the Earth is much closer to each other than is commonly believed. It looked like this: they called any person, famous or unknown, from among the 1.5 billion inhabitants of the Earth at the beginning of the 20th century, and it was necessary to build a chain of no more than five people connecting the player with this person.
Here is a typical excerpt from the story: "Okay, Selma Lagerlef, - said one of the participants in the game, - it's as easy as shelling pears." And after a couple of seconds he issued a decision: “Selma Lagerlef recently received the Nobel Prize for Literature, so she should know the Swedish king Gustav, he presented her the award during the ceremony. It is widely known that King Gustav enjoys playing tennis and participates in international competitions. He has played with White Curling as well, so they should be familiar. It so happens that I also know Curling. " (The speaker himself was a good tennis player.) “For this we needed two out of five links. And unsurprisingly, it's always easier to find someone who knows a celebrity rather than an average person. Well, give me something more difficult!"
Today this idea is known in the Russian-speaking part of the world under the name of the “theory of six handshakes”, in English it is usually called the “theory of six boundaries of separation”.
Let's find out more about this …
Experiments supporting the hypothesis
However, without experimental confirmation, this assumption remains nothing more than a game of thought. And experiments have been carried out repeatedly. First, the famous American psychologist Stanley Milgram tested the hypothesis that all people know each other through a relatively small number of intermediate connections. The experiment, staged in 1967, was called The Cramped World.
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Three hundred participants, randomly selected residents of two cities - Omaha, Nebraska and Wichita, Kansas - were to send letters to a certain stockbroker in Boston. The address was unknown, but it was possible to forward the letter through someone from your acquaintances who could theoretically know this mysterious recipient - and so on, until the letter arrived where it was needed. Each intermediate recipient-sender had to add his name in the letter so that you could track how the letter went and how long the chain was. When the results of the experiment were summed up, it turned out that the average length of the chain between the first sender and the Boston recipient was five people (or six ties - "handshakes"). In subsequent years, similar experiments were carried out more than once, under different conditions and with different initial data. They all confirmed the hypothesis.
For example, two researchers at Cornell University, Duncan Watts and Stephen Strogatz, in 1998 created a mathematical model of the "small world" and repeated Milgram's experiment on a large scale. Several tens of thousands of volunteers from all over the world took part in their experiment, and there were several endpoints - the recipients lived in different countries, in large cities and in the relative hinterland, were people of different occupations and from different social strata. In this study, letters were no longer transmitted by mail or from hand to hand, but via the Internet. The result was close to Stanley Milgram's: the average chain length was about six links. In addition, the mathematical model showed some interesting patterns of the organization of human communities: for example, that individuals play an important role in global communication,belonging to several communities at the same time.
The most large-scale study proving the hypothesis was carried out in 2006 by Yure Leskovets and Eric Horwitz from Microsoft. They analyzed the logs of the instant messaging service MSN Messenger - a total of more than 30 billion messages sent by 240 million people in 30 days (of course, all these statistics were not calculated manually, but on a computer, and the study took about two years). Without reading the texts of the messages, Leskovets and Horwitz could see the data of users: gender, age, location, who communicates how often, how voluminous his messages are, and who knows whom. The results of this study are extensive, but the main thing that interests us is that the average distance between two MSN users was 6.6 connections. This number is higher than in Milgram's experiment, but quite close to it.
On the VKontakte social network, the application ("Chain of friends - the theory of six handshakes") allows you to search for dating chains between network users. Since the VKontakte audience is limited (Russia and the CIS countries), it is not possible to achieve the same results as described above - the chains are shorter (3-4 people). However, it is interesting that chains longer than 6 people practically do not occur, which indirectly confirms the original theory.
With the ubiquity of the Internet, the principle of easy accessibility to almost anyone has become obvious. In social networks and large thematic communities - such as LiveJournal, Facebook, VKontakte, Twitter and even Wikipedia - there are services that allow you to trace the chain of mutual acquaintances from one user to another, games based on the principles of "small world", and research applications; there are also special networking projects created to further explore the possibilities of global communication.
According to the most recent experiment on this topic, today anyone can be found through social networks in just 12 hours. This was made famous by Alex Rutherford of the Masdar Institute of Science and Technology in Abu Dhabi and the Tag Challenge social game held in 2012.
The goal of the competition was to find five people in five different cities in the US and Europe. The only clues were a photograph of the person, the name of the city in which he is located, and information that he was wearing a T-shirt with the Tag Challenge logo. Alex Rutherford's team won the competition, finding three out of five men in just 12 hours.
Contrary to the traditional strategy in such situations - to tell as many different people as possible about the object of the search - Alex Rutherford's team took a different path, referring personally to those who can help in searches based on geographic data and other information available on social networks. According to the team leader, it is likely that with the right approach, finding the right person can be faster.
And yet: a scientific fact - or a myth?
Today the "six handshakes" hypothesis is widespread. It is popularized in feature films, TV shows and other phenomena of mass culture, the principle of "small world" is clearly illustrated by the social networks of the Internet, and the very idea of the availability of any person is very attractive. Who doesn't want to be a "friend of a friend" of the Queen of England or Bill Gates, Johnny Depp or Fidel Castro?..
However, the hypothesis is often misinterpreted: “I know any person on Earth through six handshakes” - that's what they usually say. But “six” is the average length of a chain, and there may be all ten or fifteen “handshakes” to some African pygmy, Tibetan monk or Polynesian fisherman, if you can build a chain at all.
The second common misconception associated with the "small world" is that after one or two levels of acquaintance we have access to a huge number of people. Each of us, suppose, has the notorious hundred friends, each of whom has a hundred more friends, etc. In fact, people tend to form closed groups: by place of residence, by occupation or work, by interests and hobbies, according to political and religious views, educational level and income level … and in fact somewhere there are caste systems with very rigid boundaries. And if you thoroughly take and count how many "acquaintances" you have, the boundaries of the social group (or several groups) to which you belong will soon be discovered, and it will become clear that at the third level you have access not to a million people, like it seemedbut only to a few thousand or tens of thousands.
In addition to the misconceptions stemming from a misunderstanding of the Six Handshake Theory, there are inherent flaws in it. Frédesh Carinti has already noticed in his story that humanity has not always been whole. If Julius Caesar, wrote Carinti, had the idea to contact one of the Aztec or Mayan priests who lived in America at the same time as him, then he would not have succeeded, it would have been impossible to build a chain between them of either five or even from three hundred links - at the time of Caesar, America was unknown to Europeans.
And now, in the 21st century, the world is far from being as monolithic and permeated with connections as one might suppose. There are still groups that are closed or almost completely isolated from the rest of the world. The Internet, which seemingly reduces connections between people, is in fact very unevenly available in different parts of the world. Consequently, the results of experiments, these "six handshakes", can be applied to Europe, to the USA, to the European part of Russia, perhaps to individual large cities, but not to the entire territory of the Earth, in different regions there will be different numbers.
Not everything is perfect with the results of the studies described above. In 2006, Judith Kleinfield, a professor of psychology at the University of Alaska Fairbanks, noticed that 95% of the letters sent during Milgram's experiment did not reach the final addressee - that is, they were simply lost somewhere halfway. She turned to the results of other similar studies and found the same thing there. So, for example, during the experiment of Watts and Strogatz, 384 out of 24,000 letters reached. “If 95-97 letters out of a hundred do not reach, can we talk about the evidence of such an experiment?” Asks Kleinfield. - Why do we believe this? The seductive idea that we live in a 'small world' where everyone knows everyone through a maximum of six intermediate acquaintances is the academic equivalent of an urban myth."
The Microsoft study, which at first glance impresses with its huge numbers (large numbers allegedly do not lie), also has its drawbacks: 4% of the world's population use the MSN messenger, and these 4% are very unevenly distributed around the planet - most of them are in the United States. In Russia, for example, ICQ used to be massively preferred over MSN. So, we again came to the conclusion that the research result is correct for a limited area, for limited groups of people, but not for humanity as a whole.
What is the "theory of six handshakes" - fact or myth, it is impossible to say for sure. The truth is most likely somewhere in between. But, one way or another, the "theory of six handshakes" is an interesting assumption, and it is likely that as we move into the future, with an increase in the density of the Earth's population, with the spread of Internet technologies and the interpenetration of cultures, people will become closer to each other.
Where did the name "six boundaries of separation" come from?
Playwright John Gueir, author of the play "Six Frontiers of Distance", with the light hand of which the hypothesis went to the masses, says that the use of the number "six" in the title of the play was prompted by the research of not Milgram, but … Guglielmo Marconi, one of the inventors of radio. In his Nobel Prize speech, Marconi said that he was able to transmit a readable message over a distance of 2,500 km. He calculated that if transmitting stations with such a transmission radius were built, then only six (more precisely - 5.83) transmitters would be required to cover the entire inhabited territory of the Earth. Gueir used this "six" as a symbol of something that encompasses the entire world.
Small world games
Among movie lovers, the game "Six Steps to Kevin Bacon" is known: you need to find a chain to Kevin Bacon from any other actor (and not necessarily a modern one, you can take the whole history of cinema). The chain is built on the principle "they were filmed together" and should not be longer than six links. It is interesting that the reason for the emergence of this game was given by Bacon himself, in one of his interviews he boastfully remarked that those with whom he was filming, in turn, were filming with all Hollywood actors. Another similar game is widespread among mathematicians, it is called "Erdos Number". The Erds number itself is the number of links in the chain of joint work from a given scientist to the Hungarian mathematician Paul Erds, known for a huge number of co-authored publications.