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Microscopic semantics and the statistics of communication

In the last chapter, we described the FOA process linguistically, in terms of words that occur in documents, morphological features of these words, structures organizing the sentences of documents, etc. We now want to treat all of these words --- which have meaning to their authors and to us reading them --- as a \rikmeaning-less stream of data - word after word after word. (Imagine it coming from some SETI radio telescope, eaves-dropping on the communication of some other planet!) We will now seek common patterns and trends to this data, using the same sorts of statistical tricks that physicists typically use on their data streams. What can we learn from looking at the statistics of our data stream, treating text as \rikmeaning-less and attempting to infer a new notion of meaning from those statistics?

But now let's narrow our focus, all the way down to the bits and characters used to represent the corpus, for example as a file on a physical device, like a hard disk. Imagine that you are an archaeologist, trying to study some civilization that had left this evidence behind. How might you interpret this modern Rosetta Stone?

Let's ignore those issues relating to the basic ASCII encoding. That is, suppose we have special knowledge of a character set. Then the frequency of these characters' occurrences would already give us a great deal of information. Anyone who has studied simple cipher techniques (or played Scrabble!) knows that a table of most frequently used letters (cf. Figure (FOAref) [Welsh88] ) can be well-exploited for breaking simple codes.

\hline Letter & Frequency\\ \hline E & .120 \\ T & .085 \\ A & .077 \\ I & .076 \\ N & .067 \\ O & .067 \\ S & .067 \\ R & .059 \\ H & .050 \\ D & .042 \\ L & .042 \\ U & .037 \\ C & .032 \\ F & .024 \\ M & .024 \\ W & .022 \\ Y & .022 \\ P & .020 \\ B & .017 \\ G & .017 \\ V & .012 \\ K & .007 \\ Q & .005 \\ J & .004 \\ X & .004 \\ Z & .002 \\ \hline \caption{English letter frequencies}

In this chapter we will move another level above characters. We will consider morphological transformations we can perform on character sequences that help us to identify root words. We will briefly mention phrases by which multiple words can be joined into simple phrasal units.

At each level we will ask very similar questions: What is our unit of analysis; i.e., just what are we counting? Then, what does the distribution of frequency occurrences across this level of features tell us about the pattern of their use? What can we tell about the meaning of these features, based on such statistics [Francis82] ?

In fact, many influential thinkers have looked at such patterns among symbols. Going back to some of our most ancient writings suggests that statistical analyses of the original Hebrew characters and their positions within the two-dimensional array of the page reveals new ``codes'' [Witztum94] [Drosnin97] .

Donald Knuth, one of computer science's most reknowned theoreticians, has analyzed an apparently random verse (Chapter 3, verse 16) from 59 of the Bible's books and used these as the basis of STRATIFIED SAMPLING of the approximately 30000 Biblical verses [Knuth90] . He found, for example, that the 3:16 verses were particulary richin occurrances of {\tt YHWH}, the ancient Hebrew name for God. Personally, Knuth found this analysis the source for ``historical and spiritual insights,'' as part of a Bible study class he lead. But speaking scientifically, how can we find meaning in text, and when are such attempts merely numerology?


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