The Small-World Problem PDF

# The Small-World Problem By Stanley Milgram 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 s...

# The Small-World Problem By Stanley Milgram 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?" Almost all of us have had the experience of encountering someone far from home, who, to, our surprise, turns out to share a mutual acquaintance with us. This kind of experience occurs with sufficient frequency so that our language even provides a cliché to be uttered at the appropriate moment of recognizing mutual acquaintances. We say, "My it's a small world." ## The Small-World Problem - **The problem:** Given any two people in the world, how many acquaintance links are needed before they are connected? - **Importance:** This is considered by many historians, political scientists, and communication specialists. It can be applied to many aspects of society, such as city planning, historical studies, and sociology. - **Two main viewpoints:** 1. **Intersecting circles of acquaintances:** Any two people can be linked in terms of intermediate acquaintances and the number of links is relatively small. 2. **Concentric circles of acquaintances:** Unbridgeable gaps exist between various groups and people within these groups will never link up. ## Visualizing the problem - **Represent people with blue dots.** - **Represent acquaintances with lines.** - **The problem:** Given two random dots, how many intermediate dots are needed to connect them? **The network spreads, with complicated interconnections.** ## Research at M.I.T. - **Average person knows 500 people.** - **Probability of two random people knowing each other:** 1 in 200,000. - **Probability of two random people sharing a mutual acquaintance:** greater than 50%. ## A Harvard Approach - **Method:** Trace a line of acquaintances linking any two people chosen at random, starting with person A and ending with person Z. - **Process:** - Person A chooses a person (B) from their circle of acquaintances and sends them a document. - Person B repeats the process. - Each document includes the name of the target person (Z) and a roster for each participant to write their name (prevents the person from returning the document to the same person). - The process continues until the document reaches a person who knows the target person. - **Results:** - The chains varied from two to ten intermediate persons. - The median was five. - **Surprising fact:** Most people estimate about 100 intermediaries are needed, demonstrating how difficult it is to grasp the power of geometric progression. ## Examining the Chains - **Key findings:** - **Females tend to send the document to other females, and males tend to send it to other males.** This suggests that certain kinds of communication are conditioned by sex roles. - **People often send the document to friends and acquaintances.** This is likely different in societies with extended kinship systems, where relatives would have a higher chance of being chosen. - **Challenges:** - **Social structure:** The study assumes random connections. However, society is not built on random connections, but is influenced by social classes and cliques. - **Inbreeding:** Many of the acquaintances of one person might be known to someone else in the chain, which means there are many redundant links. - **Possible explanations:** - **Chains are less efficient than theoretically estimated:** People may not always choose the most direct link. - **Limited acquaintances:** Participants can only send the document to one person at a time, which means they may not know the best possible intermediary. - **Chain decay:** A certain percentage of participants don't send the document on, meaning the chain ends prematurely. ## Intuition and Fact - **Most people underestimate the power of chain connections.** - **A chain is more powerful than just five links.** It includes all the links in the links, and so forth. Therefore, thousands of people are involved even if only five intermediaries are explicitly mentioned. ## Funneling - **Chains funnel toward the target person.** - **Key intermediaries:** Some people are more influential than others in passing the document on. ## The Small-World Problem and Social Structure - **Social barriers:** The study can be used to study communication patterns between different groups, such as racial groups. - **Geographic limitations:** The study suggests that distance and the flow of information between groups are not always the deciding factors, as people within certain areas may be more isolated from other groups than people in different areas despite a greater geographic distance. - **Key takeaways:** - **The small-world problem applies broadly:** The problem applies not only to humans, but to many other systems, such as communication networks and the spread of epidemics. - **The small-world problem is not just a theoretical concept:** It has practical implications for understanding social structures and how information flows. - **Further research:** - **Explore the impact of social barriers on communication:** Using the small-world model to study communication between racial groups would be insightful. - **Study the role of key intermediaries:** Examine how influential individuals connect people from different groups. ## Diagram - **Illustrates the path of a document from the starting person to the target person.** - **Shows decreasing distances with each move, indicating "funneling".** - **Highlights key intermediaries, such as **Jacobs** and **Brown**. ## Conclusions - **The small-world problem reveals more than just distance:** It provides insight into the interconnectedness of society. - **Social structures are complex and dynamic:** This study provides a framework to understand how information flows in society. - **There is much more to discover about the small-world problem:** This study is just the beginning. By continuing to explore this phenomenon, we can gain a deeper understanding of how society works.