During the 1980s techniques for analysis of geographical patterns have been refined to the point that they may be applied to data from many fields. Quantitative spatial analysis and existing functions available in geographical information systems (GIS) enable computerized implementations of these spatial analysis methods. This paper describes the application of quantitative spatial analysis and GIS functions to analysis of language data, using the extensive files of the Linguistic Atlas of the Middle and South Atlantic States (LAMSAS). A brief review of recent development of using quantitative and statistical methods for analysing linguistic data is also included.

Modern notions of language and linguistics embody a paradox, that language appears to be systematic and yet, at the same time, we know it to be variable. The paradox results when we attempt to apply rule-bound systems, the “axiom of categoricity,” to language in use, to speech as people actually use it. Taken together, the basic elements of speech correspond to what has been called a “complex system” in sciences ranging from physics to ecology to economics. Order emerges from such systems by means of self-organization, but the order that arises from speech is not the same as what linguists study as grammars. In both texts and regional/social groups, the frequency distribution of features occurs as the same curve: an asymptotic hyperbolic curve, or “A-curve.” Speakers perceive what is “normal” for regional/social groups and for text types according to the A-curve: the most frequent variants are perceived as “normal,” less frequent variants are perceived as “different,” and because particular variants are more or less frequent among different groups of people or types of discourse, the variants come to mark identity of the groups or types by means of these perceptions. Our perceptions of the whole range of “normal” variants, at any level of scale, create “observational artifacts.” That is, the grammars we describe are actually observational artifacts that come from our perceptions of the available variants, at one point in time and for a particular group of speakers, as mediated by the A-curve. Thus, the regularities we observe in speech are not the product of speakers' prior agreement on a systematic grammar, but rather what we perceive as a linguistic system is a consequence of how we perceive our language behavior.

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