Could It Be a Big World After All?
What the Milgram Papers in the Yale Archives Reveal About the Original Small World Study

 

Judith Kleinfeld
Professor of Psychology
University of Alaska Fairbanks
October 2, 2000
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Thanks to Rob MacCoun at the Goldman School of Public Policy & Boalt Hall School of Law, Univ. Calif. at Berkeley, for urging me to write up the results of my work at the Yale archives and to students at Yale University who convinced me that people would be interested.

Abstract

On the basis of evidence in the Milgram papers on the small world study, located in the Yale archives, I raise questions about Milgram's famous finding that we live in a "small world" with six degrees of separation. A renaissance of scientific interest has occurred in the "small world problem" due to a mathematical demonstration of how random connectors in a network can create a small world. Psychological research is needed to examine the empirical realities and why people have strong emotional needs to believe we live in a small, small world.

An explosion of interest in Stanley Milgram's "Small World Problem" is occurring outside the field of psychology. The stimulus is a 1998 paper in Nature which offers an intriguing mathematical explanation of how the "small world" phenomenon can be explained based on the presence of random connectors in a network (Watts & Strogatz, 1998). This fascinating mathematical demonstration, based on graph theory, is supported in the Nature article by only one empirical example from the social world: Calling two actors "connected" if they had ever been in a film together, Watts and Strogatz found that 225,000 film actors listed in the Internet Movie Database as of April, 1997 were separated from each other by only four steps. The example is intriguing and may well be a good analogy for certain other occupational networks, such as scientists or corporate businesspeople. Film actors, who shift social worlds with each film they make, however, are not a good analogy for the classic formulation of the small world problem: To what extent are people anywhere in the world connected? This problem includes illiterate farmers in rural India as well as corporate executives or teenage technophiles.

Some describe Watts' and Strogatz work on the small world problem as a "breakthrough" (Yang & Shulman, 1998) with implications as far-ranging as disease transmissions, neuroscience, and the spread of forest fires (Hayes, 2000; Yang & Shulman, 1998). The discovery triggered an explosion of media coverage and scholarly interest. "I think I've been contacted by someone from just about every field outside of English literature. I've had letters from mathematicians, physicists, biochemists, neurophysiologists, epidemiologists, economists, sociologists; from people in marketing, information systems, civil engineering, and from a business enterprise that uses the concept of the small world for networking purposes on the Internet," says Watts in an article in Discover magazine (Yang & Shulman, 1998). Although Stanley Milgram was a social psychologist, this list oddly does not include psychologists.

The "small world" problem has turned into a forgotten issue in psychology, rarely covered in textbooks and the topic of little recent research. The empirical focus of psychology and its attention to belief systems is especially needed given not only the renaissance of interest in the small world problem but also the disturbingly weak evidentiary basis of the idea that we are all connected by "six degrees of separation." The strength of popular belief that we live in a "small, small world" combined with the weakness of scientific evidence offers a fertile problem for the discipline.

In this paper, I describe my efforts to replicate Milgram’s famous "small world study" in the era of the Internet, a journey which took me to the Stanley Milgram papers on the in the Yale archives. I make three points:

1. Milgram's own empirical findings on the small world problem do not justify his famous conclusion---that we live in a "small world" where people are connected, on the average, by "six degrees of separation." Milgram's first unpublished study and unpublished attempts at replication, available in the Milgram papers, show the weakness of the evidentiary base.

2. The astonishing degree of acceptance of the notion that we are inter-connected is in itself a phenomenon important to investigate. My own exploratory research suggests that people have strong emotional needs to believe this proposition because "the belief that we are all holding hands makes you feel more secure in a scary world." Even among secular people, I was surprised to see a strong religious belief that chance meetings were not random, but evidence of some form of "Design."

3. The "small world problem," now iimportant in other disciplines, needs to be reclaimed by the discipline of psychology. Empirical research is necessary to investigate questions such as these: What does it actually mean in practical terms to be linked to others on a first-name basis? A welfare mother in New York might easily be connected to the president of the United States by a chain of six degrees: Her caseworker might be on first-name terms with her department head who may know the mayor of Chicago who may know the president of the United States. Does this matter? What kinds of people are highly connected and what kinds remain unconnected? These are precisely the kinds of situational questions that intrigued Stanley Milgram (Blass, 1992).

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The Famous "Small World Problem"

The "Small World Problem" takes its name from an experience familiar to us all. As Milgram (1967) describes it:

Fred Jones of Peoria, sitting in a sidewalk cafe in Tunis, and needing a light for his cigarette, asks the man at the next table for a match. They fall into conversation; the stranger is an Englishman who, it turns out, spent several months in Detroit studying the operation of an interchangeable-bottlecap-factory. 'I know it's a foolish question,' says Jones, 'but did you ever by any chance run into a fellow named Ben Arkadian? He's an old friend of mine, manages a chain of supermarkets in Detroit..'

'Arkadian, Arkadian,' the Englishman mutters. 'Why, upon my soul, I believe I do! Small chap, very energetic, raised merry hell with the factory over a shipment of defective bottlecaps.'

'No kidding!' Jones exclaims in amazement.

'Good lord, it's a small world, isn't it?"

This experience is so surprising, yet at the same time so familiar, that we have coined a phrase to describe it: "It's a small world" (p. 61).

The small world problem had long been an entertaining parlor game among mathematicians (Kochen, 1989) where it took this form: "Starting with any two people in the world, what is the probability that they will know each other?" Ithiel de Sola Pool at MIT and Manfred Kochen of IBM collaborated on mathematical models of the small world problem and circulated unpublished papers among an invisible college for two decades. They were reluctant to publish, Kochen (1989) explains, because "we never felt we had 'broken the back of the problem'" (p.viii). Linton Freeman convinced them to combine their working papers into a manuscript for the first issue of Social Networks. But this paper, published over twenty years after Milgram's arresting article, is still tentative and speculative, filled with questions rather than conclusions (Pool & Kochen, 1989). Milgram's work is discussed in one unenthusiastic footnote: "In the years since this essay was first written, Stanley Milgram and his collaborators (Milgram, 1967; Travers & Milgram, 1969; Korte & Milgram, 1970) have done significant experiments on the difficulty or ease of finding contact chains. It often proves very difficult indeed" (p. 4).

Few others express such caution. Milgram's "Small World Study" has slipped away from its scientific moorings and entered the world of imagination. The small world has become part of the intellectual furniture of educated people. While Milgram applied the notion of "six degrees of separation" to the American population, others apply it to the entire world.

In the flagship American Journal of Sociology, Watts (1999), for example, frames the problem this way: "Most people have at least heard of the idea that any two individuals, selected randomly from almost anywhere on the planet, are ‘connected’ via a chain of no more than six intermediate acquaintances, a notion made popular by the Broadway play (and later movie) Six Degrees of Separation " (p. 493). Milgram's phrase "Six Degrees of Separation" has become as much a part of our vocabulary as the phrase "It’s a Small World." Malcolm Gladwell (1999) calls his influential New Yorker article about the nature of social power "Six Degrees of Lois Weisberg." "Six Degrees of Kevin Bacon" has become a parlor game for movie buffs where the object is to link the ubiquitous actor with any other actor or actress through movies they have appeared in together. A web site "Six Degrees of Separation" explains it was inspired by the "theory of six degrees of separation," to create a place which would connect millions of people from around the world.

As you ride through the Small World exhibition at Disneyland, seeing costumed dolls from the countries of the world, singing in chorus the simple words to the simple tune, "It’s a Small, Small World," it is so easy to believe that what you would like to believe is true. But is the idea that we live in a small world where people are separated by an average of only six intermediaries, empirically based? Could it be not science at all but a heart-warming parable, the creation of two great showmen, Stanley Milgram and Walt Disney?

Milgram's "small world study" is one of the few studies in the social sciences that many people know and care about. Such studies, Kotre (1992) argues, quoting David Bakan, function as "scientific parables." Milgram's study of obedience to authority is a classic illustration. They combine dramatic imagery (the shock generator, a chain of people linked around the world) with a simple story line to ask a fundamental question about human nature. "The surprise ending of these experiments make them naturals for the storyteller," Kotre observes. "They slip easily from the research report into the textbook, the film, and the popular article. They become part of the mythical underpinnings of our discipline, stirring the imaginations not only of our public but of our researchers themselves" (p. 673). Milgram's "small world study," my own investigation suggests, is such a scientific parable that is, unfortunately, far from scientific.

My Journey into the Yale Archives in Search of Stanley Milgram's Original Small World Study

I had always been fascinated by Milgram's "small world study," which I regarded as one of the great, counter-intuitive studies in the social sciences. My interest in pursuing its details arose from a teaching problem. I was teaching a required course in research methods in the social sciences to graduate students in an area studies program. Most of them were history majors as undergraduates. They delighted in archival research but disliked social research. What was the point? You already knew everything from common sense, they said to me.

Thinking about how to show my skeptical students, that social research could produce counter-intuitive results, I hit upon the idea of replicating Milgram’s small world experiment in the era of the Internet. Not only were Milgram's findings counter-intuitive, but we could learn something genuinely new: Had the Internet indeed shrunk the world? In the electronic world, a virus like "Lovebug" could infiltrate people’s address books and shut down half the world’s corporations in a single day, experts estimated. Surely those of us on the right side of the digital divide were far more connected to each other, certainly in speed and probably in number of intermediate acquaintances, than Milgram had ever dreamed.

I was delighted with the potential of this project. I did not know the answer to this question. Nor would my net-savvy students, though they would have theories. Using the tools of social science research, we would find out. Along the way, we would probably come across some surprises. My ornery students would experience first-hand the joy of social research.

Reviewing the Research on the Small World Problem

To prepare for this class research project, I needed to find the original study of the small world problem so I could replicate the methodology as exactly as possible. I wanted to run one version through the mail, replicating Stanley Milgram's original study. I wanted to run a second version through e-mail, which would require adaptation of Milgram's methods. But key details of Milgram's study were unclear. What exactly had Milgram sent through the mail? Sometimes it was called a "chain-letter," sometimes a "passport," sometimes a "document in a folder." What this item actually looked like could make a significant difference in how many letters reached their target. A chain letter would be easy to discard. A "passport," on the other hand, would look like a valuable document not as easy to disregard.

I also needed to do a comprehensive review of the research literature on the small world problem and see if anyone else had updated the study in the Internet era. I realized that Milgram’s original experiment---sending a document from people in Nebraska to a stockbroker in Boston--did not in a scientific sense support the popular interpretation that people in the United States or indeed the world over were connected by an average of six intermediaries. But surely there had been numerous replications of the small world problem all over the world, I reasoned, just as there had been of Milgram’s famous study of obedience to authority. The "small world study" was so inexpensive, so easy to conduct. The Nebraska study, I learned in the archives, had cost only $680. The "small world study" raised no troubling ethical issues. I expected to find a wealth of replications right after Milgram published his sensational study.

I was in for a surprise, indeed for several surprises. For starters, I learned that Milgram had first published the study not in an academic journal but in the popular magazine Psychology Today (1967). A technical report was published two years later (Travers & Milgram, 1969). This version contained technical details glossed over in the Psychology Today publication, which was the source for popularizations such as Gladwell’s New Yorker article.

I was also disturbed by the small number of replications of the original small world study. Using as the criterion that a replication of the small world problem had to span at least two disconnected cities, I could find one, conducted by Milgram himself (Korte & Milgram, 1970). Most of the empirical research consisted of adaptations to such limited places as a college campus (Shotland,1976), businesses (Lundberg, 1975) a high-rise apartment (Bochner, Duncan, Kennedy, & Orr, 1976), or a single urban area (Lin, Dayton, & Greenwald, 1978).

To find the small world phenomenon "remarkable," the world in question must have four properties. It must be:

1) numerically large ...In the real world, n is on the order of billions,

2) sparse in the sense that each person is connected to an average of only k other people, which is, at most on the order of thousands,

3) decentralized in that there is no dominant central vertex to which most other vertices are directly connected, and

4) highly clustered, in that most friendship circles are strongly overlapping. That is, we expect that many of our friends are friends also of each other (Watts, 1999 pp. 495-496).

The replications and adaptations I was able to find did not come close to approximating these conditions. I was puzzled and disturbed.

I did find one replication of a Milgram study in the electronic age, an adaptation of Milgram’s interesting lost letter study (Stern & Faber, 1997). This replication, interestingly, did not support Milgram’s original result, that people would be less likely to send along letters if they had negative attitudes toward the addressee (communist or Nazi organizations in Milgram’s original study and Ross Perot in the e-mail replication). The study also revealed unexpected features of electronic communication compared to mail communication. While people did send the lost e-mail message back in the electronic adaptation, none sent it to the recipient. They sent the message back to the original sender

 

The Milgram Files on the Small World Problem in the Yale Archives

While reviewing the published literature, I found an article by a Yale archivist (Kaplan, 1996) reporting that Stanley Milgram's wife had given her husband's papers to the Yale archives in October, 1985, but stipulated that anything confidential was to be sealed for seventy-five years unless sanitized through an expensive procedure of removing names. Milgram's "Small World Study," I learned through e-mail correspondence with Diane Kaplan, was available for review with the exception of the data identifying subjects. I was delighted. I could see for myself what Milgram had sent through the mail---a chain-letter or a valuable-looking document. Maybe I could even find the names of two original targets---the wife of the divinity student in Milgram's first study and the Boston stockbroker who lived in Sharon, Massachusetts in Milgram's second study. What a dramatic touch it would be, I thought, worthy of Milgram himself, to replicate the study with the original targets or perhaps their children.

The Milgram papers on the "small world study" turned out to be a treasure trove of documents. The results of his first Wichita, Kansas study, I learned, had actually never been published but just alluded to in the Psychology Today article. The archives contained the original document that Milgram had sent through the mails, the newspaper advertisement from his Wichita, Kansas study, correspondence with colleagues, proposals Milgram submitted to support the small world research, and unpublished attempts at replication right after his article came out. All these documents sit in Boxes 48 and 49 of The Stanley Milgram Papers in Manuscripts and Archives at the Yale Library.

What I found was disconcerting:

1. In the first "small world study," using starters in Wichita, Kansas and an obscure target, the wife of a divinity student in Cambridge, almost no chains were completed. Only 3 of the 60 documents ever reached the wife of the divinity student. Yet Milgram's Psychology Today article featured an arresting anecdote from this first study---one letter reached the wife of the divinity student in only four days.

2. Two replications of Milgram's small world study were available in the archives. Both had been done right after his initial study but never published. Chain completion rates were so low that the researchers decided no conclusions could be drawn. I wondered how many other researchers might have made similar replication attempts but not sought publication when the data failed to support the small world theory.

3. Subtle features of Milgram's second, published experiment strongly favored chain completion. The document sent through the mail, for example, turned out to be impressive indeed: a passport of thick royal blue cardboard with the name "Harvard University" embossed in gold letters on the cover. The cover also featured a stylish gold logo. Archive correspondence showed that Milgram was well aware of the visual impressiveness of the document. He had engaged in discussion with Harvard University about the use of its name and had considered seeking legal protection for the gold logo. The roster of signatures was visually impressive, each person's name written with a fountain pen. This was certainly not a chain letter people would casually discard. The passport reminded me of the blue bank book I had treasured as a child; I kept it in my top bureau drawer and watched my savings grow. An impressive passport was not a biasing factor. But it did support the idea that people would have tried to send on the document, rather than have tossed it out.

Other features of Milgram's experiment, however, might well have biased the results. The original advertisement recruiting subjects for the Wichita, Kansas study, which I describe below, was worded so as to attract particularly sociable people. Milgram recruited subjects for the Nebraska and Los Angeles studies by buying mailing lists, an item which appeared in his proposal budget. People with names worth selling were more likely to be high income people with connections.

What I was finding in the archives actually provided more empirical support for the alternative "Big World" theory that Milgram outlines in his grant application to the Milton Fund (1966) to support his proposed study of acquaintanceship networks between whites and blacks:

There are two philosophical views on the small world problem. Some people feel that any two people in the world, no matter how remote from each other, can be linked in terms of intermediate acquaintances, and that the number of such intermediate links is relatively small.

There is, however, a contrasting view that sees unbridgeable gaps between various groups. Given any two people in the world they will never link up, because people have circles of friends that do not necessarily intersect. A message will go round in a particular circle of acquaintances, but may never be able to make the jump to another circle of acquaintances. (p. 1)

A third view combines these two theories: We live in a world with deep social cleavages. This is the theory most consistent with all the empirical research on the "small world problem."

The Original Small World Experiment Published in Psychology Today

Milgram begins his arresting article, "The Small World Problem," with a memorable illustration of his experimental success. I was a graduate student at Harvard in 1967 when I first encountered this vivid example, and I remembered it more than 30 years later. Here is the background.

Milgram's "first study" (his own label), which he terms the "Kansas Study," used starters in Wichita---a city chosen because it was "vaguely 'out there' on the Great Plains or somewhere" (p. 64). Milgram had recruited people from Wichita through a newspaper advertisement and instructed them to send a folder through a chain of people they knew on a first-name basis to the wife of a divinity student living in Cambridge, Massachusetts. Would the technique work, Milgram asks, or would the whole idea turn out to be a pipe dream?

The answer came fairly quickly...Four days after the folders were sent to a group of starting persons in Kansas, an instructor at the Episcopal Theological Seminary approached our target person on the street. "Alice," he said, thrusting a brown folder toward her, "this is for you." At first she thought he was simply returning a folder that had gone astray and never gotten out of Cambridge, but when we looked at the roster, we found to our pleased surprise that the document had started with a wheat farmer in Kansas. He had passed it on to an Episcopalian minister in his home town, who sent it to the minister who taught in Cambridge, who gave it to the target person. Altogether the number of intermediate links between starting person and target person amounted to two! (emphasis in original) (pp. 64-65 ).

In the Psychology Today article, Milgram acknowledges that this was one of the shortest chains they were ever to receive. But he never reports the results of the first study in full, either in this article or in the later technical paper (Travers & Milgram, 1969).

An undated paper, "Results of Communication Project" in the Stanley Milgram papers in the Yale archives reveals that 60 people had been recruited as starters from a newspaper advertisement in Wichita, 50 chains had been started, and that only 3 letters had made it to the wife of the divinity student: "Only 3 of these chains (or 7 1/2%) actually reached the target person; the folder passed through the hands of 8 persons on the average before reaching the target" (p. 1). This paper also shows the funneling effect found in other small world studies, due to the existence of especially well-connected people: "Two of the three completed chains went through the same people"---both wives of the deans of the Harvard Divinity School and the Episcopal Theological Seminary" (p.4).

The second Nebraska study had higher completion rates. Of 160 chains that started in Nebraska, 44 were completed and 126 dropped out, Milgram (1967) reports. But a success rate of only 28 percent means that the great majority of chains, almost three-fourths, did not get through. Moreover, Milgram calculates the success rates on the basis not of the folders he sent to the starters but on the basis of the chains that actually got started. People who did not think they could get the chain through may not have tried. As Pool and Kochen (1978) point out, such expectations of success are part of the small world problem. Either method of calculating completion rates is defensible. But success rates would have been even smaller if calculated on the basis of how many starters got passports to send out.

The Psychology Today article gives the impression that the Nebraska starters were volunteers from all walks of life, something like a random sample. But the technical report actually reports three groups of starters, all of whom would have had an advantage in reaching a Boston stockbroker (Travers & Milgram, 1969). The three groups were:

1) 100 blue chip stock owners from Nebraska

2) 96 people from Nebraska designated as the "Nebraska random" group (quotations in the original) but who were actually volunteers recruited through a purchased mailing list.

3) 100 people from Boston designated as the "Boston random" group (quotations in the original) but who were actually recruited from a newspaper advertisement.

None of these groups are good approximations to a random sample of people who might or might not have social networks linking them to a Boston stockholder who lived in Sharon Massachusetts. The blue chip stock owners in Nebraska would have had a leg up in reaching a Boston stockbroker. Furthermore, they were likely to have been high income, high status individuals whom other research on the small world phenomenon shows are more likely to complete chains (Lin, Dayton, & Greenwald, 1978; Beck & Cadamagnani, 1968 ).

The Boston volunteers came from the same city as the target. Further, they were solicited through a newspaper advertisement apt to appeal to confident and sociable people. The newspaper advertisement I found in the Yale archives (placed in the Eagle in Wichita, Kansas but probably the model for the Boston advertisement) appeals to patriotism and pride in social skills: "Could you as a typical American, contact another citizen, regardless of his walk of life?"

The Nebraska "random sample" came from a commercial mailing list (buying such a mailing list appears in Milgram’s budget request for this study in his October 6, 1995 letter to Dr. Robert Bales). The names worth selling in a mailing list are apt to be high income individuals, shown to have an advantage in making social connections.

In addition, all the subjects were volunteers, probably more sociable and open to experience than the average person. Even among these volunteers, those who did not start the chain, were not included in Milgram's calculations of success. The "random" group turns out to be far from "random" indeed.

Still, of these three groups, the best approximation to the small world problem were the Nebraska volunteers drawn from a mailing list who were trying to send passports to the Boston stockholder. Of the 96 people in this group, 76 people sent the passports out, and only 18 reached the target---a completion rate of 24 percent. Of the 100 Nebraska stockholders, 78 sent out the passports, and 24 chains were completed---a completion rate of 31 percent. Of the 100 Boston volunteers drawn from a mailing list and trying to reach a person in the same city, 63 passports were sent out and 22 reached the target---a completion rate of 35 percent.

Milgram's study of acquaintance networks between racial groups also reveals a low rate of chain completion (Korte & Milgram, 1970). White starters in Los Angeles, solicited again through mailing lists which are apt to be biased toward higher status people, tried to reach both white and "Negro" targets in the city of New York. Of the 270 chains directed at Negro targets, only 13 percent got through compared to 33 percent of the 270 chains directed toward White targets.

The explanation, as Korte and Milgram point out, was unlikely to have been racial prejudice. The Negro targets had not been identified as Negro in the passports, and data analyses did not show that the white starters were less persistent in trying to contact the Negro targets. The most probable explanation had to do with the existence of social cleavages between whites and Negroes. Another way of looking at this result is that it is not such a small world where whites and Negroes are concerned.

These results, so at variance from Milgram's notion that we live in a small world, do not appear to have led him to reconsider his theory. Why did the great majority of chains die? One possibility is that the "Big World" theory was closer to the mark. But another possibility was methodological problems with the study: people could have gotten connected if they had tried but they just didn't bother. This was the view Milgram took in the original Psychology Today article. Later researchers accepted it. In their review of the literature on the "small world problem," for example, Bernard & Kilworth (1979) quote with approval Hunter and Shotland's (1974) assessment: If a folder gets lost, "it probably doesn't mean that you can't get from A to B but that some intermediary was careless, hostile, or hopeless" (p. 322). Milgram (1967) and others (e.g. White, 1970; Hunter & Shotland, 1974; Kilworth & Bernard, 1979) sought a mathematical fix: By using observed chain length and making a variety of untested or poorly tested assumptions, they estimated how long the chains would have been without attrition.

But such mathematical modeling simply assumes the conclusion---that we do live in a small world.

Unpublished Studies of the "Small World Problem" In the Milgram Papers

The Milgram papers in the Yale archives contain two unpublished studies of the type I had been expecting to find---efforts to replicate Milgram’s work in another location after the publication of the exciting findings in the original Psychology Today article in 1967.

The first study was done by Michael Beck and Paul Cadamagnani at John Carroll University, titled "The Extent of Intra-and Inter-social group contact in the American Society," and dated May, 1968. Beck and Cadamagnani recruited 151 volunteers from Crestline, Ohio, divided into low income, middle income, and high income groups. The starters were to try to reach a low income, middle income, or high income person in Los Angeles. But the low chain completion rate was a disappointment: "Since the completion rate was so low (less than 18%), no statistically significant conclusions can be made" (p.4). The study noted an extremely important point: No low-income senders were able to get complete chains to people other than other low-income people. The high income group stood out: They were far more willing to participate in the experiment at all and far more apt to get their messages through.

The second unpublished study, "Small World Phenomenon Investigated on the Basis of Social Extroversion" by Carol Kelliher, Pat McLaughlin, Frances Rudkin, and Leo McIsaac at the University of Massachusetts at Boston is undated but appears to have been done sometime between 1969 and 1970 since it refers to the Korte and Milgram study, published in 1970, as "In press." Arbitrarily selected individuals in Boston, Massachusetts, Charlottetown, Prince Edward Island and Springvale, Maine used Milgram's "small world method" to generate chains to targets in small Massachusetts towns. The purpose was to study the effect of social extroversion on the number of steps from starter to target. But the low success rate was again disappointing: Only 4 of the 58 chains (7% ) reached their target. Little can be made of these results, however, since this experiment suffered from such problems as the researchers lacking money to provide stamps and envelopes to the participants.

 

Studies of the Small World Problem in the Published Research Literature

The Milgram papers at the Yale archives contained a curious paper with no author. Dated 8/8/79 and titled "It’s a Small World After All," the paper looked like someone had sent it to Milgram for review prior to publication. The paper described in great detail a variety of other small world experiments that I had not located in an electronic literature search. Using clues in the paper, I was able to locate the author---Eugene Garfield, who was interested in scientific networks and went on to publish an abbreviated version of this valuable paper later that year (Garfield, 1979).

The Garfield paper drew my attention to one study published in a European journal (Guiot, 1976) which was not consistent with the basic pattern---low chain completion rates in any attempt to link starters and targets over a substantial geographic distance. This study, I found, had used an ingenious adaptation of the Milgram small world method. Instead of using the mail, Guiot used the telephone. Each potential starter was called on the telephone by the researcher and asked to participate, using a telephone network. If a person dropped out, the chain was reactivated by calling back the previous person and asking that person to select a new contact to restart the chain.

Whether this novel procedure conforms to the theoretical nature of the small world problem is dubious since people who did not telephone another contact, despite prodding from the researcher, may well have been more isolated individuals. As support for the "small world phenomenon" the study has other problems. The study involved only one city and its purpose was to investigate ethnic gatekeeping. The starting persons were 52 French Canadian volunteers in Montreal who were instructed to reach a Jewish target, the Vice-Principal of a Jewish day school who lived in a Montreal suburb. Guiot's success rate was extraordinarily high (85%). But this study may only demonstrate that Jews in Montreal live in a small world: Once you got to a Jew, you could get your message through.

Interestingly, studies of places which actually were small worlds, such as Shotland's (1976) study of Michigan State University sometimes revealed high rates of chain completion. For faculty to faculty chains at Michigan State, for example, the proportion of faculty who reached other faculty targets was 93 percent; administrators had target success rates of 97 percent. Students, a larger and more diffuse group, had lower rates of completion, but student to student chains still had a completion rate of almost 50 percent.

But the only study of the small world phenomenon I could find in the published literature, other than those of Milgram and his colleagues, that even came close to spanning more than one city was Lin, Dayton, & Greenwald's (1978) study of a single urbanized area in the Northeast. The point was to investigate social stratification, particularly barriers between whites and blacks. Of 596 packets sent to 298 volunteers, 375 packets were forwarded and 112 eventually reached the target---a success rate of 30 percent. But the pattern demonstrates the existence not of a small, small world but of social barriers between racial groups. "Communication flows mainly within racial groups," the authors conclude. "Crossing the racial boundary is less likely to be attempted and less likely to be effective" (p.118).

Taken as a whole, small world studies suggest we live in neither of the two worlds about which Milgram theorizes: 1) a small world, where people are connected, or 2) a big world, where people are alienated from each other, each confined to their own circles. The empirical data suggest a combination: We live in a lumpy world, rather like a badly cooked bowl of oatmeal. Some people, who are more apt to be high status, high income, and white, are well-connected. Other people, who are likely to be lower status and black, are not. The empirical research does not suggest a world where we are all connected, separated by only "six degrees of separation." Milgram's findings are not a counter-intuitive triumph of social research. They reveal a all-too-familiar pattern---that we live in a world where social capital, the ability to make connections, is rare and more apt to be held by an elite.

What Are We To Think About Stanley Milgram, One of the Great Heroes of the Social Sciences?

As I read through the Stanley Milgram correspondence in the Yale Archives, I could not avoid thinking about a question I did not want to ask: Who was Stanley Milgram, a man I had always considered one of the greatest psychologists of his generation? In his thorough and insightful analysis of Stanley Milgram's significant contributions in so many fields , Blass (1992) draws attention to Milgram's focus on everyday observation as a basis for developing problems, his emphasis on experimentation, his attention to the way different situations affect outcomes, and his attention to the moral and philosophical questions at the heart of important research problems. How could such a researcher have neglected the evidence contradicting his theory?

After reading through Milgram's correspondence, the marginal notes he made on manuscripts sent to him, his review of other people's proposals concerning the small world phenomenon, I came away with a strong sense that Stanley Milgram was a careful, meticulous man, tough-minded, socially skilled, and exquisitely attentive to details. On certain ethical matters, perhaps he approached the line, but the issues were small and he stayed far from the border. For example, Harvard University refused permission to use the Harvard name on the passport. But Milgram got around the prohibition by using the Harvard name on the passport as part of the identifying address. His grant application to Dr. Robert Bales requesting funds for his Nebraska study overstates his success: "10 percent of the initiated chains have been completed and the completion of several other chains is imminent" (p. 3). Yet, only 3 of the 50 folders which started out from Wichita were ever completed so 10 percent would have been an overestimation. But this amounted to minor puffing in a research proposal.

In his published research, Milgram clearly reported the small number of completed chains, with the exception of the first Kansas study. This failure to report could be easily rationalized: The first study could have been seen as a pilot study. My judgment from the archives was that Milgram was a man who would stack the experimental deck in his favor in every way he could think of, but he would not misrepresent his results. Would he mislead? Possibly so. Blass (1992) points out that Milgram failed to report the quantitative outcomes of certain conditions in the obedience studies----a problem similar to his failure to report publicly the first results of the Small World study.

Why then did Milgram trumpet the finding that Americans were connected by six degrees of separation? My view is that Milgram himself was carried away with his own findings, especially the way the magic number "six" or close approximations to it kept coming up as the mean chain length. He did not stand back from his data and seriously consider the possibility that he was wrong, that his theory was wrong. Instead, he figured the problem was a limitations in his methods, and he immediately sought out a mathematician to find a fix (White, 1970). Milgram, I suspect, was as beguiled by his own results as any of us.

Our Desire To Believe We Live in a "Small, Small World"

The speed with which both researchers and the general public accepted Milgram’s results as confirming the small world phenomenon, despite so little supporting evidence, raises an intriguing question: Why do we want so much to believe that we live in a small, small world? Why do we take such delight in the experience of meeting a stranger and finding we know someone in common? I was amazed at the passion with which highly educated people I knew described their own "small world" experiences and how strongly they believed they did live in a small world, despite what any social scientist might find. Intrigued by their conviction, I asked them about the basis for their belief.

They offered two reasons. First, belief in the small world gave them a sense of security. "It’s a scary world out there," one female federal judge told me, "It’s good to believe that we are all somehow holding hands." Second, many people, I was surprised to find, interpreted the small world phenomenon in religious terms. These people were not academics but they were highly educated. They saw such events---like meeting a person who knew your college roommate whom you had lost touch with and putting you back in touch---as evidence not of chance but of Design. Their beliefs were based on faith, not reason. Milgram's research supported their belief structure and no critique, including this one, would dislodge it.

As I listened with care to the small world experiences which people delighted in telling me, I was struck by a third explanation for people’s belief in a small world. This explanation combines a point about overlapping social networks among the educated elite that Ithiel de Sola Pool makes forcefully in the introduction to the original paper (Pool & Kochen, 1989) with a mathematical formulation of the small world experience different from the one he envisioned. Most people had just one or two small world experiences, I found, which they lovingly recounted. One person, for example, told me of his surprise at finding his third grade classmate on a train in Belgium. (The person telling this story admitted that he was less surprised when he met her again that summer at the American Express office in Rome and then again in Geneva). But how likely would it be, for people who travel in similar social networks, never to meet anyone anywhere anytime that they had had a connection with in the past? Coincidences do occur. The two great investigators of the small world problem, Stanley Milgram and Ithiel de Sola Pool, both died in the same year---1984---Milgram of a heart attack and de Sola Pool of cancer (Kochen, 1989).

Overlapping specialized social networks make such coincidences less surprising. Ithiel de Sola Pool made this point in his original discussion with dramatic force (Pool & Kochen, 1989):

The senior author's favorite tale happened in a hospital in a small town in Illinois where he heard one patient, a telephone lineman, say to a Chinese patient in the next bed: "You know, I've only known one Chinese before in my life. He was a _____from Shanghai." "Why that's my uncle," said his neighbor. The statistical chances of an Illinois lineman knowing a close relative of one of (then) 600,000,000 Chinese are minuscule; yet that sort of event happens.

The patient was, of course,not one out of 600,000,000 random Chinese, but one out of the few hundred thousand wealthy Chinese of Westernized families who lived in the port cities and moved abroad. Add the fact that the Chinese patient was an engineering student, and so his uncle may well have been an engineer too---perhaps a telecommunications engineer..Far from surprising the encounter seems almost natural (p. 6).

But the issue goes beyond this important point concerning overlapping social networks. The "small world problem" that de Sola Pool and Stanley Milgram were investigating does not have the same mathematical structure as the "small world experiences" that people delighted in telling. The expression "small world" was the same; the phenomenon was not. The "small world problem" is expressed mathematically in such forms as: What are the chances that two people chosen at random from the population will have a friend in common? But the "small world experiences" I was hearing about would be expressed mathematically in this form: What is the probability that you will meet a friend from your past or a stranger who knows a mutual friend from your past over the course of your lifetime? What would be remarkable is if this never happened, especially in view of the overlapping social networks of highly educated people.

I did not attempt to replicate Milgram’s small world experiment in the electronic age. The main reason was that my students were not interested. In the age of the Internet, they took for granted that they could find anyone fast. That does not mean that their beliefs, the parables of their own generation, are true. Let me offer two examples. First, after the semester had ended, I found in progress an electronic mail replication of the Small World Study. On June 30, 2000, Mike Wilson, a reporter for the St. Petersburg Times, told hisreaders he was attempting "a grand social experiment" to see "what would happen if we conducted a version of Milgram's experiment in the Internet age." His target person was "Tara," a young woman working in the computer industry in Portland, Oregon. The senders were six men and women from different parts of the country, Honolulu, Tampa, and Portland, Oregon, and they could send the first message to many people (unlike the original Milgram study). They predicted that Tara would get the message within a week and Wilson promised to publish the results of their experiment in six weeks. On August 13, 2000, he reported, alas, that Tara never got the message---any of them. Some intermediaries ignored the e-mail message, which they saw as spam, not sociology (Wilson, 2000). But Wilson had evidence from his instructions to send e-mails back to him that thousands of copies of their original note were in circulation and some had gotten close to her. Perhaps Tara, as an individual, was not well-connected, Wilson speculated: "Like most of us, she has a few close friends and a modest number of acquantances she keeps up with." But the possibility that most of us may live in a big world, after all, did not occur to him.

Second, I did succeed in finding in the Milgram papers in the Yale archives the name of the wife of the divinity student from Milgram's first study and the name of the Boston stockbroker from his second study. I do not reveal their names for ethical reasons. Both gave permission to Stanley Milgram for their names to be made public on the passports; they have not given their permission to me. Using the many cost-free peoplefinder services on the Internet as well as the services of long distance operators with telephone books at their disposal and telephone calls placed to people with the same name, I tried to find them. I could locate neither.

The Internet may have shrunk the world. But we may still live in a bigger world than our modern myths lead us to believe. One of the critical functions of social research is falsifying ideas we deeply wish to be true. Psychology as a discipline can illuminate why we cherish such beliefs and how our beliefs in themselves affect whether the world is big or small.

REFERENCES

Beck, M., & Cadamagnani, P. (1968). The extent of intra- and inter-social group contact in the American society. (Available from The Stanley Milgram Papers, Manuscripts and Archives, Yale University, New Haven, Conn.)

Bernard, H. R., & Kilworth, P. D. (1979). A review of small world literature. Sociological symposium 28: 87-100.

Blass. T. (1992). The social psychology of Stanley Milgram. Advances in Experimental Social Psychology 25: 277-329.

Bochner, S., Duncan, R., Kennedy, E., & Orr, F. (1976). Acquaintance links between residents of a high rise building: An application of the "small world" method. The Journal of Social Psychology 100: 277-284.

Fienberg, S. E., & Lee, S. K. (1975). On small world statistics. Psychometrika 40: 219-228.

Garfield, E. (1979). "It's a small world after all". Current Contents 43: 5-10.

Gladwell, M. (1999, January, 11). Six degrees of Lois Weisberg. The New Yorker: 52-63.

Guiot, J. M. (1976). A modification of Milgram's small world method. European journal of social psychology 6: 503-507.

Hayes, B. (2000, January--February). Graph theory in practice: Part 1, American Scientist 88.

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Hunter, J. E., & Shotland, R. L. (1974). Treating data collected by the "small world" method as a Markov process. Social Forces 52.

Kaplan, D. E. (1996). The Stanley Milgram papers: A case study on appraisal of and access to confidential data files. The American archivist 59: 288-297.

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Kilworth, P. D., & Bernard, H. R. (1979). A pseudomodel of the small world problem. Social Forces 58: 477-505.

Kochen, M., Ed. (1989). The small world. Norwood, N.J., Ablex.

Korte, C., & Milgram, S. (1970). Acquaintance links between White and Negro populations: Application of the small world method. Journal of Personality and Social Psychology 15(2): 101-108.

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Lin, N., Dayton, P., & Greenwald, P. (1978). The urban communication network and social stratification: A "small world experiment". In B. D. Ruben (Ed.), Communication yearbook : Volume 1. (pp. 107-119) New Brunswick, Transaction Books.

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Milgram, S. (1967). The small-world problem. Psychology Today 1: 61-67.

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Results of communication project (undated). (Available from The Stanley Milgram Papers, Manuscripts and Archives, Yale University, New Haven, Conn.)

Shotland, R. L. (1976). University communication networks: The small world method. New York, Wiley.

Stern, S. E., & Faber, J. E. (1997). The lost e-mail method: Milgram's lost-letter technique in the age of the Internet. Behavior Research Methods, Instruments & Computers 29: 260-263.

Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry 32: 425-443.

Watts, D. J. (1999). Networks, dynamics, and the small-world phenomenon. American Journal of Sociology 105: 493-527.

Watts, D. J. & Strogatz. S. H. (1998). Collective dynamics of 'small-world' networks. Nature 393: 440-442.

White, H. C. (1970). Search parameters for the small world problem. Social Forces 49: 259-264.

Wilson, M. (August 13, 2000). Pondering six degrees of separation. St. Petersburg Times (http://www.sptimes.com/News/081300/Floridian/Pondering_six_degrees.shtml)

Yang, J. & Shulman, P. (1998). From Muhammad Ali to Grandma Rose. Discover 19: 84-89.

 

 

 

 

 

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