Passage
Read the full passage. Bracketed letters like [A] mark the four positions for the insert-text question.
The Small-World Phenomenon
¶1 Two strangers who meet by chance can find they know someone in common. Neither one expected any connection at all. This pattern has a name: the small-world phenomenon. It happens when any two people are linked through only a short chain of acquaintances. It shows up in ordinary conversation, whenever two people discover a friend in common. In 1929, long before anyone tested the idea, the Hungarian writer Frigyes Karinthy made a guess. He suggested that any two people on Earth might be connected through a chain of only about five acquaintances. At the time, the claim sounded entertaining, not something anyone could actually measure.
¶2 The striking part of the small-world phenomenon is that these chains are supposed to stay short. That is true even though the world holds an enormous number of people. If each person knows a few hundred others, the number of possible paths between any two strangers multiplies almost without limit, yet the actual shortest chain rarely runs longer than half a dozen steps. That property is difficult to confirm. No single person can see the whole map of who knows whom across an entire country, let alone the planet. Testing Karinthy's claim would mean tracing real chains of acquaintance through thousands of people at once. For decades, no one had a practical way to do that.
¶3 Researchers eventually found two different ways to test the claim. In 1967, the psychologist Stanley Milgram mailed folders to volunteers in Nebraska. He asked each volunteer to send it toward a specific stockbroker in Boston. The rule was simple: give it only to someone you know personally. [A] Each volunteer added their name to the folder before passing it along, so the finished chains could be counted step by step. [B] Many folders never reached their target, but the ones that did had passed through about five and a half people on average. [C] Decades later, researchers tested the same idea with a different kind of record: the network of friendships on Facebook. [D] That network connects hundreds of millions of accounts to one another. Measuring the shortest online path between random users produced an average distance of about four and a half steps. Two very different methods, one built from paper and mailboxes and the other from computer records, had arrived at nearly the same number.
¶4 The consistency of that result changed how scientists think about large networks. It suggested that short chains are not a special feature of human friendship, but a general property of many kinds of networks. Examples include power grids, computer networks, and the paths along which diseases spread through a population. In this way, a simple guess made by a Hungarian writer in 1929 grew into a tool that shapes fields well beyond sociology. It now helps engineers design efficient transportation systems and helps researchers predict how quickly information, or misinformation, can travel through an entire population.
- acquaintance: a person you know but who is not a close friend
- stockbroker: a person whose job is to buy and sell stocks for other people
Questions
11 questions — every TOEFL Reading question type, in test order.
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Highlighted: "If each person knows a few hundred others, the number of possible paths between any two strangers multiplies almost without limit, yet the actual shortest chain rarely runs longer than half a dozen steps."
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It was a surprisingly short number for a country as large as the United States.
Where would the sentence best fit?
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The small-world phenomenon is the surprising finding that two strangers are usually connected through only a short chain of acquaintances, and two very different research methods have confirmed that this short-chain pattern is real.