Network Structures and Vocabulary Acquisition in a Foreign Language
The starting point for this paper has nothing to do with vocabulary. It is in fact a classical study in social psychology, carried out by Stanley Milgram (Milgram, 1967). Milgram was interested in what has come to be known as the ‘small world problem’ — the curious coincidences which occur whenever groups of strangers meet, and find that they have acquaintances in common. From a purely statistical point of view, the fact that strangers have acquaintances in common is not so surprising as it feels when it happens in real life. Take a large country, say the USA with a population of about 250 million, and assume that everybody is acquainted with about 1,000 other people. Given these starting assumptions, the probability of two random people already knowing each other works out at about 1 in 100,000. However, the probability of their having a friend in common is much higher than this, about 1 chance in 100. The chances of two strangers (call them A and D) being connected by a chain of two acquaintances (A knows B who knows C who knows D) is better than 99 chances in 100.
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