Sometimes, in places far away from your homeland, you may accidentally meet someone who was friends with your parents, or sat at the same Desk with one of your colleagues, or was the boss of your former boss. "The world is small," they usually say in such cases. How far can such a chain of mutual acquaintances stretch? Is it possible to access the Queen of England, for example, through friends of my friends?
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 consist of a certain number (namely, five) links was formulated by the Hungarian writer Friedes Karinti. His short story, written in 1929, was called "Links of the chain". The story was about a game, a thought experiment designed to prove that The earth's population 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 XX 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: "all Right, Selma Lagerlof," said one of the participants in the game,"this is a piece of cake." And after a couple of seconds, he issued a decision: "Selma Lagerlof recently received the Nobel prize in literature, so she must know the Swedish king Gustav, who presented her with the award during the ceremony. It is widely known that king Gustav likes to play tennis and participates in international competitions. He had a chance to play with the White Curling, so they should be familiar. I happen to know Curling, too." (The speaker was not a bad tennis player himself) "It took us two links out of five. And no wonder, it's always easier to find someone who knows a celebrity than an ordinary person. Well, give me something more complicated!»
Today, this idea is known in the Russian-speaking part of the world as the "theory of six handshakes", while in English it is commonly called the "theory of six boundaries of distance".
Experiments confirming the hypothesis
However, without experimental evidence, this assumption remains nothing more than a game of thought. The experiments were carried out repeatedly. First, the hypothesis that all people know each other through a relatively small number of intermediate connections was tested by the famous American psychologist Stanley Milgram. The experiment, set in 1967, was called "Close world".
Where did the name "six boundaries of distance" come from?»
The playwright John Guair, author of the play "Six lines of distance", with whose light hand the hypothesis (previously nameless and known only in academic circles) went to the masses, says that the use of the number "six" in the name of the play was prompted by research not by Milgram, but by... Guglielmo Marconi, one of the inventors of radio. In his Nobel prize speech, Marconi said he was able to transmit a readable message over a distance of 1,551 miles. He calculated that if transmitting stations were built with such a transmission radius, then only six (5.83, to be more precise) transmitters would be needed to cover the entire inhabited territory of the Earth. Guair used this "six" as a symbol of something that spans the entire world.
Three hundred participants, randomly selected residents of two cities - Omaha, Nebraska, and Wichita, Kansas-were to send letters to a stockbroker in Boston. The address was unknown, but it was possible to forward the letter through someone you knew who could theoretically know this mysterious recipient and so on, until the letter arrived in the right place. Each intermediate recipient-sender had to add their own name to the message so that they could track how the message 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 is five people (or six connections - "handshakes"). In the following years, similar experiments were conducted more than once, under different conditions and with different initial data. All of them confirmed the hypothesis.
For example, two researchers at Cornell University, Duncan watts and Steven Strogatz, created a mathematical model of the "small world" in 1998 and repeated Milgram's experiment on a large scale. Several tens of thousands of volunteers from all over the world participated 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 sent by mail or hand-to-hand, but via the Internet. The result was close to that of Stanley Milgram: the average chain length was about six links. In addition, the mathematical model showed some interesting patterns in the organization of human communities: for example, that an important role in global communication is played by individuals belonging to several communities at the same time.
The most extensive study proving the hypothesis was conducted in 2006 by Jure Leskovec and Eric Horwitz from Microsoft. They analyzed the logs of the MSN Messenger instant messaging service a total of more than 30 billion messages sent to 240 million people in 30 days (of course, all these statistics were calculated not manually, but on a computer, and the study took about two years). Without reading the texts of messages, Leskovets and Horvitz could see user data: gender, age, location, who communicates how often, how large their messages are, and who knows whom. The results of this study are extensive, but the main thing that we are interested in 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.
With the ubiquity of the Internet, the principle of easy accessibility for almost anyone has become obvious. In social networks and large thematic communities such as Facebook, VKontakte, Twitter, and even Wikipedia-there are services that allow you to trace the chain of common acquaintances from one user to another, games based on the principles of "close world", and research applications; there are also special network projects created to further explore the possibilities of global communication.
The game "close the world»
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 entire history of cinema). The chain is built on the principle of "they were filmed together" and should not be longer than six links. Interestingly, the reason for the emergence of this game was given by bacon himself, who boastfully noted in an interview that those with whom he starred, in turn, starred with all Hollywood actors. Another similar game is common among mathematicians, it is called "Erdos Number". Actually, the Erdos number is the number of links in the chain of joint works from a given scientist to the Hungarian mathematician Paul Erdos, known for a huge number of co-authored publications.
Still, is it a scientific fact or a myth?
Today, the "six handshakes" hypothesis is widely accepted. It is popularized in feature films, TV shows and other phenomena of mass culture, the principle of "close peace" is clearly illustrated by Internet social networks, and the idea of accessibility of any person is very attractive in itself. Who doesn't want to be a "friend of 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 anyone on Earth through six handshakes" - so they usually say. But "six" is the average length of a chain, and an African pygmy, a Tibetan monk, or a Polynesian fisherman may be all ten or fifteen "handshakes" away, if the chain can be built at all.
Another Stanley Milgram experiment
Stanley Milgram is known not only for "close world". In 1963, he set up and described another experiment (later named after him), investigating the willingness of people to cause suffering to other people.
There were three participants in the experiment: a" teacher "(the subject himself), a" student "(an actor whom the subject considered to be the same as himself, a person from the street), and an" authority " (a researcher). The subject was told that this was an experiment investigating the ability to remember; the "student" was put in the next room, then the "teacher" gave him mnemonic tasks from the list and in case of an incorrect answer had to press a button to punish the "student" with an electric discharge. With each subsequent mistake, the impact force had to be increased: in front of the "teacher" there was a whole row of buttons signed "Weak impact", "medium impact", " Caution! Shock hazardous to health", "XXX", etc., and, in addition, the voltage was specified, from 15 to 450 V. In fact, there was no electricity. But the buttons crackled naturalistically when pressed, and the "student" actor first screamed, then began to swear, knock on the wall, begged to stop tormenting, cried, and after the most severe blows fell silent-as if losing consciousness or dying.
It was the responsibility of the "authority" to insist on continuing the experiment, without threats, without persuasion or bribes – just in a neutral tone to say "please continue" or something like that. The task of the experiment was to track at what "tension" the subject will cease to obey the "authority".
It was assumed (before the experiment, and Milgram interviewed 39 psychiatrists) that no more than 20% would bring the tension to half the scale, and it was unlikely that anyone would even carry out the execution to the end. The results of the experiment were amazing: of the 40 subjects studied, all went far beyond half the scale, and 65% even got to 450 V. Subsequently, the experiment was repeated many times in different countries and with different participants, and everywhere the percentage of people who were ready to go to the end was from 61 to 66%.
The second common misconception associated with the" small world " is that after just one or two levels of Dating, we have access to a huge number of people. Each of us, let's say, has the notorious hundred friends, each of whom has another hundred friends, and so on. in fact, people tend to form closed groups: by place of residence, by occupation or work, by interests and Hobbies, by political and religious beliefs, by educational level and income level... but somewhere there is a caste system with a very rigid boundaries. And if you thoroughly take up and calculate how many "familiar acquaintances" you have in total, you will soon discover the boundaries of the social group (or several groups) to which you belong, and it will become clear that on the third level you have access not to a million people, as it seemed, but only to several thousand or tens of thousands.
In addition to the misconceptions that arise from a misunderstanding of the" six handshake theory, "there are also shortcomings in the" six handshake theory " itself. Already Prides Carenti in your story noticed that mankind was not always consistent. If Julius Caesar, Carinti wrote, had thought of contacting one of the Aztec or Mayan priests who lived in America at the same time as him, he would have failed, it would have been impossible to build a chain of five or even three hundred links between them in Caesar's time, America was unknown to Europeans.
And now, in the twenty-first century, the world is far from being as monolithic and permeated with connections as one might expect. There are still closed or almost completely isolated groups from the rest of the world. The Internet, which seems to reduce communication between people, is actually very unevenly available in different parts of the world. Therefore, the results of the experiments, these "six handshakes", can be applied to Europe, to the United States, to the European part of Russia, perhaps to individual large cities, but not to the entire territory of the Earth, in different areas there will be different numbers.
The results of the studies described above are also not perfect. In 2006, Judith Kleinfeld, a Professor of psychology at the University of Alaska Fairbanks, noticed that 95% of emails sent after the Milgram experiment did not reach the final destination that is, they simply got lost somewhere in the middle. 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? Kleinfeld asks. Why do we believe that?" The tempting 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."
Whether the "six handshake theory" is a fact or a myth, it is impossible to say for sure. The truth is probably somewhere in the middle. But anyway, the "six handshake theory" is an interesting suggestion, and it is likely that as we move into the future, with the increase in the density of the Earth's population, with the spread of the Internet and the interpenetration of cultures, people will become closer to each other.
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 consist of a certain number (namely, five) links was formulated by the Hungarian writer Friedes Karinti. His short story, written in 1929, was called "Links of the chain". The story was about a game, a thought experiment designed to prove that The earth's population 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 XX 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: "all Right, Selma Lagerlof," said one of the participants in the game,"this is a piece of cake." And after a couple of seconds, he issued a decision: "Selma Lagerlof recently received the Nobel prize in literature, so she must know the Swedish king Gustav, who presented her with the award during the ceremony. It is widely known that king Gustav likes to play tennis and participates in international competitions. He had a chance to play with the White Curling, so they should be familiar. I happen to know Curling, too." (The speaker was not a bad tennis player himself) "It took us two links out of five. And no wonder, it's always easier to find someone who knows a celebrity than an ordinary person. Well, give me something more complicated!»
Today, this idea is known in the Russian-speaking part of the world as the "theory of six handshakes", while in English it is commonly called the "theory of six boundaries of distance".
Experiments confirming the hypothesis
However, without experimental evidence, this assumption remains nothing more than a game of thought. The experiments were carried out repeatedly. First, the hypothesis that all people know each other through a relatively small number of intermediate connections was tested by the famous American psychologist Stanley Milgram. The experiment, set in 1967, was called "Close world".
Where did the name "six boundaries of distance" come from?»
The playwright John Guair, author of the play "Six lines of distance", with whose light hand the hypothesis (previously nameless and known only in academic circles) went to the masses, says that the use of the number "six" in the name of the play was prompted by research not by Milgram, but by... Guglielmo Marconi, one of the inventors of radio. In his Nobel prize speech, Marconi said he was able to transmit a readable message over a distance of 1,551 miles. He calculated that if transmitting stations were built with such a transmission radius, then only six (5.83, to be more precise) transmitters would be needed to cover the entire inhabited territory of the Earth. Guair used this "six" as a symbol of something that spans the entire world.
Three hundred participants, randomly selected residents of two cities - Omaha, Nebraska, and Wichita, Kansas-were to send letters to a stockbroker in Boston. The address was unknown, but it was possible to forward the letter through someone you knew who could theoretically know this mysterious recipient and so on, until the letter arrived in the right place. Each intermediate recipient-sender had to add their own name to the message so that they could track how the message 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 is five people (or six connections - "handshakes"). In the following years, similar experiments were conducted more than once, under different conditions and with different initial data. All of them confirmed the hypothesis.
For example, two researchers at Cornell University, Duncan watts and Steven Strogatz, created a mathematical model of the "small world" in 1998 and repeated Milgram's experiment on a large scale. Several tens of thousands of volunteers from all over the world participated 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 sent by mail or hand-to-hand, but via the Internet. The result was close to that of Stanley Milgram: the average chain length was about six links. In addition, the mathematical model showed some interesting patterns in the organization of human communities: for example, that an important role in global communication is played by individuals belonging to several communities at the same time.
The most extensive study proving the hypothesis was conducted in 2006 by Jure Leskovec and Eric Horwitz from Microsoft. They analyzed the logs of the MSN Messenger instant messaging service a total of more than 30 billion messages sent to 240 million people in 30 days (of course, all these statistics were calculated not manually, but on a computer, and the study took about two years). Without reading the texts of messages, Leskovets and Horvitz could see user data: gender, age, location, who communicates how often, how large their messages are, and who knows whom. The results of this study are extensive, but the main thing that we are interested in 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.
With the ubiquity of the Internet, the principle of easy accessibility for almost anyone has become obvious. In social networks and large thematic communities such as Facebook, VKontakte, Twitter, and even Wikipedia-there are services that allow you to trace the chain of common acquaintances from one user to another, games based on the principles of "close world", and research applications; there are also special network projects created to further explore the possibilities of global communication.
The game "close the world»
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 entire history of cinema). The chain is built on the principle of "they were filmed together" and should not be longer than six links. Interestingly, the reason for the emergence of this game was given by bacon himself, who boastfully noted in an interview that those with whom he starred, in turn, starred with all Hollywood actors. Another similar game is common among mathematicians, it is called "Erdos Number". Actually, the Erdos number is the number of links in the chain of joint works from a given scientist to the Hungarian mathematician Paul Erdos, known for a huge number of co-authored publications.
Still, is it a scientific fact or a myth?
Today, the "six handshakes" hypothesis is widely accepted. It is popularized in feature films, TV shows and other phenomena of mass culture, the principle of "close peace" is clearly illustrated by Internet social networks, and the idea of accessibility of any person is very attractive in itself. Who doesn't want to be a "friend of 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 anyone on Earth through six handshakes" - so they usually say. But "six" is the average length of a chain, and an African pygmy, a Tibetan monk, or a Polynesian fisherman may be all ten or fifteen "handshakes" away, if the chain can be built at all.
Another Stanley Milgram experiment
Stanley Milgram is known not only for "close world". In 1963, he set up and described another experiment (later named after him), investigating the willingness of people to cause suffering to other people.
There were three participants in the experiment: a" teacher "(the subject himself), a" student "(an actor whom the subject considered to be the same as himself, a person from the street), and an" authority " (a researcher). The subject was told that this was an experiment investigating the ability to remember; the "student" was put in the next room, then the "teacher" gave him mnemonic tasks from the list and in case of an incorrect answer had to press a button to punish the "student" with an electric discharge. With each subsequent mistake, the impact force had to be increased: in front of the "teacher" there was a whole row of buttons signed "Weak impact", "medium impact", " Caution! Shock hazardous to health", "XXX", etc., and, in addition, the voltage was specified, from 15 to 450 V. In fact, there was no electricity. But the buttons crackled naturalistically when pressed, and the "student" actor first screamed, then began to swear, knock on the wall, begged to stop tormenting, cried, and after the most severe blows fell silent-as if losing consciousness or dying.
It was the responsibility of the "authority" to insist on continuing the experiment, without threats, without persuasion or bribes – just in a neutral tone to say "please continue" or something like that. The task of the experiment was to track at what "tension" the subject will cease to obey the "authority".
It was assumed (before the experiment, and Milgram interviewed 39 psychiatrists) that no more than 20% would bring the tension to half the scale, and it was unlikely that anyone would even carry out the execution to the end. The results of the experiment were amazing: of the 40 subjects studied, all went far beyond half the scale, and 65% even got to 450 V. Subsequently, the experiment was repeated many times in different countries and with different participants, and everywhere the percentage of people who were ready to go to the end was from 61 to 66%.
The second common misconception associated with the" small world " is that after just one or two levels of Dating, we have access to a huge number of people. Each of us, let's say, has the notorious hundred friends, each of whom has another hundred friends, and so on. in fact, people tend to form closed groups: by place of residence, by occupation or work, by interests and Hobbies, by political and religious beliefs, by educational level and income level... but somewhere there is a caste system with a very rigid boundaries. And if you thoroughly take up and calculate how many "familiar acquaintances" you have in total, you will soon discover the boundaries of the social group (or several groups) to which you belong, and it will become clear that on the third level you have access not to a million people, as it seemed, but only to several thousand or tens of thousands.
In addition to the misconceptions that arise from a misunderstanding of the" six handshake theory, "there are also shortcomings in the" six handshake theory " itself. Already Prides Carenti in your story noticed that mankind was not always consistent. If Julius Caesar, Carinti wrote, had thought of contacting one of the Aztec or Mayan priests who lived in America at the same time as him, he would have failed, it would have been impossible to build a chain of five or even three hundred links between them in Caesar's time, America was unknown to Europeans.
And now, in the twenty-first century, the world is far from being as monolithic and permeated with connections as one might expect. There are still closed or almost completely isolated groups from the rest of the world. The Internet, which seems to reduce communication between people, is actually very unevenly available in different parts of the world. Therefore, the results of the experiments, these "six handshakes", can be applied to Europe, to the United States, to the European part of Russia, perhaps to individual large cities, but not to the entire territory of the Earth, in different areas there will be different numbers.
The results of the studies described above are also not perfect. In 2006, Judith Kleinfeld, a Professor of psychology at the University of Alaska Fairbanks, noticed that 95% of emails sent after the Milgram experiment did not reach the final destination that is, they simply got lost somewhere in the middle. 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? Kleinfeld asks. Why do we believe that?" The tempting 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."
Whether the "six handshake theory" is a fact or a myth, it is impossible to say for sure. The truth is probably somewhere in the middle. But anyway, the "six handshake theory" is an interesting suggestion, and it is likely that as we move into the future, with the increase in the density of the Earth's population, with the spread of the Internet and the interpenetration of cultures, people will become closer to each other.
