Zipf’s Law, proposed by an American Linguist named George Kingsley Zipf, deals with probability. It states the the frequency of an event (f) is inversely proportional to its rank (r).
Originally, it was proposed for the frequency of words used in the English language. A word’s approximate usage is determined by the formula: f(r)≅0.1/r
The most common word (Rank 1) in the English language is “the”, which, in a typical text, occurs about one-tenth of the time. The second most common English word (Rank 2) is “of”, which occurs approximately one-twentieth of the time, and so on and so forth.
To look at it another way, focus only on the rank: 1/rank means that world occurs 1/rank of the time. The word “the” occurs 1/r times, the word “of” occurs half that amount (Because 1/rank for the second word is equivalent to ½). The third word occurs one -third as often as the second word (1/rank equals ⅓). And the forth word occurs ¼ as often. Unfortunately, beyond the ranking of 1,000 the law becomes untrue.
This same principle can be applied to other things. Though the results are not exactly correct, it comes up with a decent estimate. For example, the largest city in a country is about twice the size of the second largest. The second largest city is about three times the size of the third largest, and so on. The basic principle can be useful in schemes like urban planning.
For more information, visit: http://www.britannica.com/topic/Zipfs-law
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