A Complex Systems Approach to Language Patterning Andrew Wedel University of Arizona April 10, 2008

Similarity relationships provide analogical pathways of change Learning and reproduction are not perfectly accurate. Ability to store and reproduce experienced variation allows ‘biased error’ to influence the trajectory of change  ‘imagination in the system’. –Biases in variation amplify over many cycles of usage and acquisition (e.g., Pierrehumbert 2001, Blevins 2004, Wedel 2006, Griffiths 2007)

Positive feedback Analogical Bias: Any trend in variation toward greater similarity along any cognitively salient dimension can promote pattern entrenchment: ‘local analogy’ (Joseph 1996) –The notion of local analogy is central to many complex-systems analyses of language patterns: individually small-scale, local analogical biases on variation promote development of long- range, coherent patterns at a higher level of analysis. (e.g., Wedel 2006, see also Blevins 2004). –Conceptually parallel to Darwin’s insight that variation in reproductive success that is insignificant on the individual level can result in population-wide changes that look ‘purposeful’.

Negative Feedback Contrast maintenance –Any form of pressure to maintain contrast between differently signifying forms will act as a brake on the simplifying effects of similarity-bias (Wedel 2007, in prep).

Simulation as a tool for exploring complexity Allows us to test hypotheses in a simpler system that still contains the feedback interactions that are proposed to underlie some pattern. –What interactions are sufficient to produce a given pattern type?

Illustration: Constrained phoneme inventory emerges through competing biases 2 agents in conversation Each has a lexicon consisting of four CV word categories. –C and V are defined along single dimensions e.g., VOT, height –Categories are populated by experienced exemplars. The choice of four CV words is made to allow individual word- exemplars to be represented as points on a graph. Perception/production link: agents biased toward reproducing what they have heard (e.g., Goldinger 2000, Oudeyer 2002).

Three feedback pathways Positive –Variation in production is biased toward frequently experienced local variants at two levels: 1.Sound level (e.g., Nielsen 2007) 2.Word level (Goldinger 2000) Negative –Competition between lexical categories in listener categorization promotes contrast maintenance (Wedel 2004, Blevins and Wedel 2009).

Roadmap to the following graphs The x- and y-axes represent single V and C dimensions, respectively, for example vowel height and VOT. –Each CV lexical exemplar can therefore be represented as a point on a graph. The color of each lexical exemplar indicates its lexical category: red, green, yellow, blue. Each of the following movies represents a single simulation with some subset of the three feedback pathways included. –At the beginning of each simulation, each lexical category is seeded with random lexical exemplars.

Simulation 1: no negative feedback promoting contrast In this simulation, there is nothing that acts against word- or sound-level homophony. As a result, incremental positive feedback from similarity bias drives all word- and sound- exemplars into mono-modal distributions, i.e, homophony. This results in: –a phoneme inventory with one consonant and one vowel. –a lexicon with one CV form mapped to four lexical categories.

Simulation 1: no negative feedback promoting contrast Vowel height Consonant VOT Click on graph to see movie

Simulation 1: no negative feedback promoting contrast Vowel height Consonant VOT pa

Simulation 2: no positive feedback at the sound level In this simulation, we include negative feedback promoting word-level contrast, and positive feedback promoting similarity at the word-level......but no positive feedback at the sound-level. Because there is no representation at the sound- level, each word evolves idiosyncratically. This results in: –a phoneme inventory with four consonants and four vowels. –a lexicon with four distinct CV words mapped to four lexical categories.

Simulation 2: no positive feedback at the sound level Vowel height Consonant VOT Click on graph to see movie

Simulation 3: Positive feedback at word and sound levels; Negative feedback for contrast In this simulation, all three feedback pathways are included. –Positive feedback promotes maximal similarity within both word- and sound- levels. –Negative feedback promotes contrast at the word-level. This results in a system of ‘constrained phonemic contrast’: –a phoneme inventory with two consonants and two vowels. –a lexicon with four distinct CV words mapped to four lexical categories.

Simulation 3: Positive feedback at word and sound levels; Negative feedback for contrast Vowel height Consonant VOT Click on graph to see movie

Simulation 3: Positive feedback at word and sound levels; Negative feedback for contrast Vowel height Consonant VOT pipa biba

Summary of Model Elements 1.Multiple interacting levels of representation Word, sound 2.Positive feedback through local analogical bias 3.Negative feedback through contrast maintenance at the word level

Outcomes 1.Contrast maintenance at the lexical level promotes contrast at the sound level. 2.Positive feedback at the sound level constrains contrast at the sound level: promotes evolution of a constrained phoneme inventory.  Provides an account for sound-contrast as parasitic on word-contrast (see Martinet 1955, King 1967, Surendran and Niyogi 2003).