Small World Experiment

The experiment in the small world comprises several experiments carried out by social psychologist Stanley Milgram in his research on social networks in the United States . What was innovative about this research was the revelation that human society is a social network that presents the structure of the small world , characterized by much shorter interconnections than expected. Experiments are often associated with the theory of the six degrees of separation , although Milgram never used this term personally.

Historical context of the phenomenon of the small world

It is very likely that Marconi’s conjectures , based on his radio work in the early twentieth century and articulated in his Nobel Prize- winning speech in 1909, have inspired the Hungarian author Frigyes Karinthy to write, among many other things, a challenge To find another person with whom he could not be connected, by a maximum of five people. This is probably the earliest reference to the concept of six degrees of separation, and the search for a solution to the mathematical problem of the small world .

The mathematician Manfred Kochen , an Austrian who had experience in the state urban design, and the political scientist Ithiel de Sola Pool wrote a mathematical manuscript titled “Contacts and Influences” (Contacts and Influences), while working at the University of Paris , early Of the 1950s , during a period in which Stanley Milgram visited and collaborated with his investigations. The manuscript, which circulated among academics for over 20 years before being published in 1978, formally articulated the mechanics of social networks , exploring its mathematical consequences (including their degrees of connectivity). The manuscript left several significant unresolved questions regarding social networks, one being the number of degrees of separation in real social networks. Stanley Milgram took up the challenge of his return from Paris, conducting the experiments published in the article “The Small World Problem”, in the popular scientific journal Psychology Today, and with a more rigorous version published in Sociometry two years later. Psychology Today generated a huge amount of publicity for the experiments, which are remembered even today, long after much of the training has been forgotten.

The Stanley Milgram experiment was conceived in an era in which a number of independent research lines coincided with the idea that the world was becoming increasingly interconnected. Michael Gurevich had done seminal work in his empirical study of social networking structure in his dissertation for the Ph.D. in Research at the Massachusetts Institute of Technology under the tutelage of Ithiel de Sola Pool .

The mathematician Manfred Kochen extrapolated these empirical results in “Contacts and Influences,” concluding that “In a population similar in size to the United States , with no social structure, it is practically a fact that two individuals Can contact each other, through at least two intermediaries. In a [socially] structured population, this is less feasible, but still seems likely. And perhaps for the world population, it would probably only be necessary to add one more individual. “Subsequently Montecarlo simulations were built , based on Gurevich’s data, which recognized that to model a social structure, both strong and weak interpersonal connections were needed. The simulations, carried out on computers in 1973, were limited, but they were still able to predict that there was a somewhat more realistic average of three degrees of separation among the population of the United States, a value that foreshadowed Stanley’s findings Milgram.

Stanley Milgram revisited Gurevich’s experiments on interpersonal networking, when he carried out a widely publicized sequence of experiments, which began in 1967 at Harvard University . Milgram’s most famous work is a study of obedience and authority, widely known as the Milgram Experiment . Milgram’s early association with Sola Pool and Kochen was probably the source of his interest in the growing interconnection between humans. Gurevich’s interviews served as the basis for Milgram’s experiments on the phenomenon of the small world . This was the same phenomenon articulated by the writer Frigyes Karinthy in the 1920s, while documenting a widely held belief in Budapest that individuals were separated by six degrees of social contact. This observation, in turn, was loosely based on the demographic seminal work of state agents who greatly influenced the design of Eastern European cities during that same period. Benoit Mandelbrot , a mathematician born in Lithuania, who had traveled extensively throughout Eastern Europe, was aware of state empirical rules and was also a colleague of Sola Pool, Kochen and Milgram at the University of Paris during the early part of the decade 1950 (Kochen led Mandelbrot to work at the Institute for Advanced Studies and later IBM in the United States ). The circle of researchers was fascinated by the interconnectivity and “social capital” of human networks. The results of Milgram’s studies showed that people in the United States seemed to be connected by about three bonds of average friendship, with no speculation about global ties. Due to the wide publicity that the article published in the journal Psychology Today gave to the experiments, the notion of Six Degrees has been erroneously attributed to both Stanley Milgram and Manfred Kochen and Frigyes Karinthy; However, the most likely is that the term six degrees of separation has been popularized by John Guare, who attributes the figure ‘six’ to Marconi.

The experiment

The Milgram experiment generated a desire to learn more about the likelihood that two randomly selected people would know each other. This is one way of approaching the problem of the small world . An alternative view of the problem is to imagine the population as a social network and try to find the average length of the connection between any two nodes. The Milgram experiment was designed to measure the length of these connections, developing a procedure to count the number of links between any two people.

Basic procedure

  1. Although the experiment underwent a series of variations, Milgram typically chose individuals in the North American cities of Omaha , Wichita, and Boston to be the beginning and end of a chain of correspondence. These cities were selected because they represented a great distance in the United States, both geographically and socially.
  2. Individuals from randomly selected Omaha and Wichita were sent packets of information. These included letters detailing the purpose of the study, and background information about the recipient to be contacted in Boston. They also contained a list in which the participants had to register their names, and pre-addressed response cards to Harvard .
  3. Along with receiving the invitation to participate, the individual was asked if he or she personally knew the recipient described in the letter. If so, the person should forward the letter directly. For study purposes, meeting someone “personally” was defined as a you-to-yourself relationship.
  4. In the case – more likely – that the person did not know personally the recipient, the person had to think of a friend or relative whom they knew personally, and who was more likely to know personally the recipient. The first person then had to enter his name on the list and forward the package to the second person. A response card should also be sent to Harvard researchers so that they could track the chain’s progress toward the recipient.
  5. When the packet finally reached the recipient, the investigators could examine the list to count the number of times it had been forwarded from person to person. In cases where packets never reached the recipient, researchers could identify the breaking point of the chain, thanks to the received cards.

Results

Shortly after starting the experiments, the packets began to reach the recipients and the researchers started receiving participants’ cards. In some cases, the packets reached their recipient in just one or two steps, while some strings were composed of up to nine or ten links. However, a significant problem was that, on many occasions, people refused to forward the packets, causing them to fail to reach the recipient. In one case, 232 of the 296 packets sent never reached their destination.

However, in the 64 cases in which the packets did eventually reach their addressees, the average length of the connection chain fluctuated between 5.5 and 6 people. Based on this, the researchers concluded that the population of the United States was separated by about six people on average. Thus, although Milgram never personally used the term six degrees of separation , his findings possibly contributed greatly to the diffusion and acceptance of that concept.

In an experiment in which 160 packages were shipped, 24 reached its recipient in Sharon, Massachusetts . Of those 24, 16 were delivered to the recipient by the same person, whom Milgram calls “Mr. Jacobs, “a clothing dealer. Of those who were received at the workplace, at least half were delivered by two other men.

The researchers used the cards to qualitatively examine the types of strings created. Generally, the package quickly reached a geographic proximity, but circulated around the recipient almost at random, until finding its inner circle of friends. This suggests that the participants strongly favored the geographical characteristics when choosing the most appropriate person to continue the chain.

Reviews

There are a number of methodological critiques made to the Milgram Experiment of the Small World, which suggest that the average length of the chains of contacts may actually be longer or shorter than Milgram estimated. Four of these criticisms are summarized below.

  1. In the article “The Six Degrees of Separation ‘Myth,” it is argued that Milgram’s study shows irresponsible selectivity and prejudice because of the way in which the participants were If a constant percentage of “no responses” is assumed for each chain, the longer chains would be underestimated, since it is more likely to find people unwilling to participate. Therefore, the Milgram experiment underestimates the true length of the chains of contacts.
  2. One of the key features of Milgram’s methodology is that participants were asked to choose a person from their acquaintances whom they considered most likely to know the recipient. This means that, in many cases, the participant could not be sure which of their friends was the best person to continue the chain. Thus, because participants in the Milgram experiment did not have a topological map of the social network, they might actually be sending the packet further away from the recipient, rather than sending it down the shortest path. This can create a slight bias and overestimate the average number of ties needed to connect two randomly chosen people.
  3. The description of heterogeneous social networks still remains an open question. Although no research was done in the area for several years, in 1998, Duncan J. Watts and Steven Strogatz published an article that represented a major step forward in the journal Nature.
  4. It is impossible for the entire world population to be interconnected by only six degrees of separation, since there are certain populations that have never had contact with people outside their own culture, such as the Sentinelese in the Andaman Islands . However, the Sentinelese population is currently estimated at 250 people, representing only 0.000000038% of the planet’s population. It is therefore possible to think that more than 99% of the world’s population can be connected in this way, since it would require at least 66,000,000 isolated people to make up 1% of the Earth’s population.

Influences

The social sciences

Based on articles originally published in The New Yorker , Malcom Gladwell elaborated the concept of “funneling” (“bottleneck”). Gladwell argues that the phenomenon of the six degrees of separation depends on a few extraordinary people (“connectors”), with extensive networks of contacts and friendships. These nodes mediate connections between the vast majority of individuals who would otherwise be loosely connected.

However, recent work on the effects of the small-world phenomenon on disease transmission has indicated that, owing to the nature of strong social network connections, suppressing these major nodes in a population often has little effect on average length Of connection between individuals.

Mathematicians and actors

Smaller communities such as mathematicians or actors have found that they are densely connected, through chains of personal or professional contacts. The mathematicians have created the Erdős Number to indicate how far they are from Paul Erdős , based on the publication of articles together.

A similar exercise has been done with actor Kevin Bacon , for actors who have participated in productions with him, which later became the popular game ” Six Degrees of Kevin Bacon .” The The Oracle of Bacon website uses the social networking data available on the Internet Movie Database , in order to determine the number of links between actor Kevin Bacon and any other subject celebrity. There is also the combined modality, the Number of Erdős-Bacon, for those actors-mathematical and mathematical actors.

Players of the popular Asian game Go describe their distance from the great player Honibo Shusaku, counting his “Number of Shusaku”, which counts the degrees of separation through the games that the players have had.

Current research on the phenomenon of the small world

The problem of the small world is still today a popular research topic, on which many experiments are still being carried out. For example, the “Small World Project” was recently held at Columbia University in New York , USA , which sought to generate a version of the same experiment based on sending emails, and Which managed to find average connection lengths of about five people on a global scale. However, the same criticisms of Milgram’s experiment on the small world are applicable to this research.

Network models

In 1998, Duncan J. Watts and Steven Strogatz , both in the Department of Theoretical and Applied Mechanics of Cornell University, published the first model of a network of contacts, referring to the phenomenon of the small world . Both showed that both the natural world networks and those of the man-built world show the ownership of the small world, as in the case of neural networks of Caenorhabditis elegans , and electric energy transport networks . Watts and Strogatz showed that starting with a regular frame, the addition of a small number of random links reduced the diameter-the direct path between any two vertices of the network-from a very long to a very short one. The research was originally inspired by Watts’ efforts to understand the synchronization of the sounds emitted by crickets , as they show a high degree of coordination during long stretches, as if led by an invisible guide. The mathematical model developed by Watts and Strogatz to explain this phenomenon has since been applied in a wide range of different areas. In the words of Watts himself:

I believe that I have been contacted by one person from every existing field, except that of English literature. I have received letters from mathematicians, physicists, biochemists, neurophysiologists, epidemiologists, economists, sociologists; Of people in the area of ​​marketing, information systems, civil engineering, and a company that works under the concept of the small world for networking networking purposes.

Duncan J. Watts , From Muhammad Ali to Grandma Rose

Overall, the model demonstrated the certainty of Mark Granovetter’s observation that it is “the firmness of weak ties” that holds the social network together. Although the specific model has been generalized by Jon Kleinberg , it still stands as a canonical case in the field of complex networks . In the area of ​​network theory, the idea presented by the Small World Network Model has been extensively explored. In fact, several classic results in Random Graph theory show that even networks that do not have a real topological structure present the phenomenon of the small world , which is expressed mathematically as the diameter of the network, growing with the logarithm of the number Of nodes (instead of growing proportionally to the number of nodes, as is the case of regular grids).

In computer science , the small-world phenomenon (although it is not typically called that) is used in the development of secure peer-to-peer protocols, Internet routing algorithms and ad-hoc wireless networks, and The search for algorithms for communication networks of all kinds.

Milgram’s experiment in popular culture

The subject of social networks pervades popular culture in the United States and elsewhere. In particular, the notion of the six degrees of separation has become part of the collective consciousness. Virtual communities such as Friendster , MySpace , Facebook and Orkut , among others, have greatly increased the connectivity of online space, through the application of the concept of social networks .