We have a grand history of measuring the earth about us. Why can't we measure language? I think it is because we have trouble coming to grips with the analogy between points and words. So I propose the analogy of a numeric coordinate for a point is the native meaning of a word and that the analog of the abstract point is a word's noun/adjective/verb role within a narrative structure.
This may seem awkward since the word meaning is generally qualitative not quantitative. But I think that is the right way to go and you can always turn a qualitative space into a quantitative one - eg a color space. And this way narrative structure built around word roles takes center stage in the abstract "geometric" discussion of semantics.
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