The ubiquity of data obeying Zipf's Law has made it a lightning rod, attracting a number of ``explanations.'' More, these explanations come from an extremely impressive set of original thinkers, from widely ranging disciplines: \item Noam Chomsky, the most influential linguist of the last 30 years; \item George Miller, the mathematical psychologist famous for such insight as the ``$7\pm2$ chunks'' of memory limitation; \item Herbert Simon, the Nobel Prize winning economist and one of the fathers of artificial intelligence; \item Benoit Mandelbrot, the computational physicist most famous for his work on fractals.
Herbert Simon, a keen observer of much cognitive activity, suggests the ubiquity of Zipf's Law across heterogeneous collections should make us somewhat suspicious of its ability to address the ``fine structure'' of linguistics: No one supposes that there is any connection between horse kicks suffered by soldiers in the German army and blood clots on a microscope slide other than that the same urn scheme provides a satisfactory abstract model of both phenomena. It is in the same direction that we shall look for an explanation of the observed close similarities among the five classes of distributions listed above. [Simon55] \eq (With ``urn'' Simon is referring to mathematical models, e.g., related to Poisson processes.\dhfoot{Poisson processes} See §3.2.1.3 for more on the ``five classes'' of Simon's models.)
We therefore begin this section by reviewing a number of early attempts to explain the phenomena underlying ZIpf's Law; its mathematical derivation is reserved for Chapter 5.
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FOA © R. K. Belew - 00-09-21