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Summary

This historical background is provided because the stories of these eminent scientists stories remain compelling. The plausibility of the proposed theories, coupled with our retrospective knowledge of their incorrectness, also provides a sobering background as we attempt to infer semantic properties from the statistics arising in FOA. As we shall discuss in Chapter 5 (cf. Section §5.1 ), the real basis of Zipf's Law can be traced to much simpler mechanisms relating only to patterns of characters rather than any underlying semantics or purposes, is sufficient to derive this generalized form of Zipf's Law. Mandelbrot, and then George Miller and Noam Chomsky, have shown that the underlying phenomena relating a word's frequency to its rank order is obeyed as much by random text -- generated by monkeys at typewriters, for example -- as it is by other samples of text (the Bible, James Joyce's Ulysses, etc.) we tend to find more literate.

The fact that the simple, four-character sequence {ZIPF} should bring together such a rich combination of mathematical and semantic issues is ironic to say the least. There is obviously a great deal we can predict about our language by assuming nothing more than we would about monkeys at keyboards. At the same time, the fact that we can change the meaning of a simple sequence of characters, for example the title of this section {\tt REMEMBER ZIPF}, so dramatically by adding a single additional character to form either {\tt REMEMBER ZIPF!} or {\tt REMEMBER ZIPF?} should also make it clear how much more there is still to say.


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