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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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