A Complex Systems Approach to Language Patterning

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

2. 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)

3. 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’.

4. 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).

5. 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?

6. 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).

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

8. 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.

9. 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.

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

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

12. 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.

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

14. 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.

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

16. Simulation 3: Positive feedback at word and sound levels; Negative feedback for contrast pi pa bi ba Consonant VOT Vowel height

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

18. Outcomes • Contrast maintenance at the lexical level promotes contrast at the sound level. • 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).