The next toolkit

Language is an example of collective behavior, and it is a type of collective behavior for which people are highly adapted. Comparable systems in other creatures in no way approach the level of organization found in human languages. Language provides a canonical example of a complex system: robust, adaptable, and selfassembling. Self-assembly occurs both in the cognitive system (as children bootstrap a complex generative system from limited and varied exposure to its manifestations) and in populations, as people match their language systems to each other, and group themselves into social networks of people who share the same language. Linguistic systems arise within the affordances of physics, biology, and society. Take vowels as an example. The fact that vowels can be well characterized using three formant trajectories (disregarding all resonances of the vocal tract above the third one) derives from several facts. One is that the glottal source spectrum rolls off rapidly, with the result that upper formants are not reliably excited. Another is that the hearing systems of people and all other animals effectively compute a spectral representation of the sound, from which the resonances of the sound source can be estimated. Yet another is that the auditory system is most sensitive right in the region of the first three formants. The confluence of these factors as the phonetic grounding of the vowel map is discussed at more length in Pierrehumbert (2000). Not all combinations of three resonances correspond to possible vowels, of course; the entire threedimensional vowel space is effectively circumscribed by the articulatory range of human beings. Thus, physics and biology define a vowel solid, much as the color vision system defines a color solid. Specific languages preferentially exploit different regions of this solid. For example, the region corresponding to cardinal [u] is not exploited in many dialects of American English. In the American South, the closest correspondant to [u] is much fronter; Labov, Ash, and Boberg (2006) report F2 values in the range of 1400–2000Hz for this region. Fronter than cardinal [u], but not as front as French /y/, the Southern AE [u] corresponds to a particular region in the three-dimensional vowel space, much as the color word ‘‘teal’’ corresponds to a particular region of the color solid which may not have a precise label in some other languages. Now, we can also consider the cluster of people who share any given variant of /u/. In a dialect atlas, such as Labov et al. (2006), the areas in which a variant predominates are marked as regions on a map. Of course this