The Zipf file

The word “the” is the most commonly used word in the English language. The second most used word is “of” and it occurs half as many times as “the.” The third most used word, “and,” occurs a third as many times, the fourth most used word, “a,” occurs a fourth as many times, and so on down through the whole English language.

This pattern is called Zipf’s Law, named for George Kingsley Zipf, an American linguist who popularized the pattern and sought to explain it.  Zipf claimed that Zipfian distribution applies to a lot of things.  

For example, he claimed the largest city in a country is roughly twice as populous as the second largest city, three times as large as the third largest, four times as large as the fourth largest, and so on.  This isn’t always true, but the pattern appears surprisingly often.  It is a rule of thumb, like the Pareto Principle.

Is this really a law?  If so, why?  What are the implications?  One of them, it seems to me, is that all other things being equal, there will be a drift towards extreme income inequality – which doesn’t mean that extreme income inequality is inevitable or justified.  What do you think?

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