Zipf's law and the structure and evolution of languages

By using a vast number of examples in social and economical data including natural languages, George Zipf was able to show an amazingly robust functional form of the rank-frequency plots 11, f 1=r f for frequency, r for rank, now commonly called Zipf's curve or Zipf's law. George Miller, a renowned linguist, summarized this study in 1965: Faced with this massive statistical regularity, you have two alternatives. Either you can assume that it reeects some universal property o f human mind, or you can assume that it represents some necessary consequence of the laws of probabilities. Zipf chose the synthetic hypothesis and searched for a principle of least eeort that would explain the apparent equilibrium between uniformity and diversity in our use of words. Most others who were subsequently attracted to the problems chose the analytic hypothesis and searched for a probabilistic explanation. Now, thirty y ears later, it seems clear that the others were right. Zipf's curves are merely one way to express a necessary consequence of regarding a message source as a stochastic process" 2. Miller based his comment on the work of Mandelbrot 3 who rst proved the Zipf's law i n monkey-typing" texts by minimizing the average cost of transmitting information. Later, Miller showed that the least-cost part is not really necessary in the proof 44 the cause of the Zipf's law in random texts is purely statistical. Here was how he summarized it: It seems, therefore, that Zipf's rule can be derived from simple assumptions that do not strain one's credulity unless the random placement of spaces seems incredible, without appeal to least eeort, least cost, maximal information, or any other branch of the calculus of variations. The rule is a simple consequence of those intermittent silences which w e imagine to exist between successive w ords" 44. Another thirty y ears have passed. Do we h a ve a n y new evidence that Zipf's explanation of the Zipf's law in natural language by least-eeort principle is more correct than a statistical explanation? Zipf's explanation was reiterated in a Commentary by Tsonis, Schultz and Tsonis TST 55. TST argues that random texts are not relevant to natural languages for the purpose of proving Zipf's law because: 1 all combinations of letters are considered as possible words in random texts but not for natural languages; 2 the frequency of occurrence of a word is a …