Dynamics, speech timing, and grammar Louis Goldstein USC and Haskins Laboratories ! The language of dynamical systems can provide a principled link between qualitative states and quantitative observables. This insight has led to the use of such systems in modeling aspects of cognition over the last 20 years (Turvey 1990, Kelso 1995; Tulleret al., 1994; Gafos & Benus, 2006). One property of nonlinear dynamical systems that holds particular potential for linguistic theory (in both syntax and phonology) is that qualitatively distinct forms (corresponding to different phonetic forms in syntax or phonology) can emerge in a principled fashion from the same dynamical law in different contexts, where those contexts set different initial conditions for the system or set the values of the system's control parameters differently. This kind of application of abstract dynamics to syntax engaged some of Jean-Roger's thinking over the last year or two of his life. In this talk, I will present some of the parallel applications to phonology along the lines outlined below. ! Dynamics of timing in speech production: clocks, coupling and entrainment. A challenging issue in speech production is understanding how the minimal units of speech production (e.g., gestures in the articulatory phonology of Browman & Goldstein, 1992) are coordinated with one another in time, so as to achieve both stability (consistent timing for a given phonological form) and flexibility (changes in timing due to prosody and speaking conditions, such as rate). Some simple models will be shown to be inadequate. For example, sequential chains which unit n+1 is triggered when unit n reaches some phase of its articulatory motion (or its acoustic consequences) fail because they could not generate geminate consonants, for example, in which an articulatory-acoustic state is sustained for a phonologically controlled interval of time. An alternative in which successive events are triggered on the ticks of single central sequence generator (as has been demonstrated for songbirds, Fee et al., 2004) fails to capture the observation that the variability in relative timing between units is not uniform and, in fact, differs as a function of syllable structure and other factors (Byrd, 1996). A possible solution developed over the last several years (Nam & Saltzman, 2003; Saltzman et al., 2008) will be presented that hypothesizes that there are multiple clocks (roughly, each gestural unit is associated with its own clock that is responsible for triggering it) and that stability is achieved by the coupling the clocks to one another in phonologically-specific ways. Coupled clocks (nonlinear oscillators) exhibit entrainment which results in stable patterns of relative timing that can flexibly adjust to global or local changes in rate. ! Dynamics and representation: syllable structure as coupling graph. Pairs of coupled nonlinear oscillators can entrain in either of two qualitatively distinct modes of phase-locking: in-phase and anti-phase (180° out of phase). Experiments (Haken et al, 1985; Turvey, 1990) have shown that both of these modes are immediately accessible when participants are asked to oscillate multiple limbs synchronously; no learning is required. Of the two, the in-phase mode is the more accessible and more stable. When

oscillation rate increases, spontaneous shifts from anti-phase to in-phase are observed. These modes form the basis for a dynamical representation of syllables structure (Goldstein et al, 2006; Nam, 2007). Syllable structure is represented as a coupling graph in which the nodes are the clocks that trigger speech gestures and the edges are coupling specifications. Onset consonant gesture clocks are coupled in-phase to the nucleus gesture clocks, while nucleus clocks are coupled anti-phase to coda gesture clocks. Multiple gestures in an onset or a coda are coupled in eccentric (not intrinsically accessible) phases that require learning. The resulting graph topologies can account for both qualitative (phonological) and quantitative (phonetic) properties of syllables, several of which will be presented: universals of syllable structure, language-particular syllabification differences, timing variability, and properties of geminate consonants. In addition, this model predicts that in particular speaking contexts, the mode of oscillator entrainment resulting from grammatically specified coupling may become less stable than some intrinsic, non-grammatical mode of entrainment. This can explain a common type of speech error, namely gestural intrusions (Goldstein et al, 2007). ! Other grammatical regularities as dynamical laws. Beyond timing and phase, other grammatical properties can be expressed by nonlinear dynamical equations that define the possible attractor states for some system order parameter other than relative phase (Gafos and Benus, 2006). For example, main phrase prominence in English can occur either finally or pre-finally. This can be expressed (Nava, 2010) by a dynamical system that governs the relative prominence of the final constituent vs. some pre-final constituent and has a potential function with two stable basins (attractors): one or the other constituent can be more prominent (but they cannot be equal). In any particular utterance, the basin into which the system settles is determined by the biasing introduced by other relevant dynamical laws. An account of the allomorphy of the regular English past-tense along these lines will be presented (Goldstein, in press). References Browman, C. P. & Goldstein, L. (1992). Articulatory phonology: an overview. Phonetica, 49, 155–180. Byrd, D. (1996). Influences on articulatory timing in consonant sequences. Journal of Phonetics, 24, 209-244. Fee, M.S., Kozhevnikov, A.A. & Hahnloser, R.H.R. (2004). Neural mechanisms of vocal sequence generation in the songbird. Ann. N.Y. Acad. Sci. 1016, 153–170 Gafos, A. & S. Benus. (2006). The dynamics of phonological cognition. Cognitive Science 30, 5, 905-943. Goldstein, L., Byrd, D., and Saltzman, E. (2006) The role of vocal tract gestural action units in understanding the evolution of phonology. In M. Arbib (Ed.) From Action to Language: The Mirror Neuron System. Cambridge: Cambridge University Press. pp. 215-249. Goldstein, L, Pouplier, M., Chen, L., Saltzman, E., and Byrd, D. (2007). Dynamic action units slip in speech production errors. Cognition, 103, 386-412.

Goldstein, L. (in press). Back to the past tense in English. In Bravo, R., Mikkelsen, L., & Potsdam, E. (Eds.), Representing language: Essays in honor of Judith Aissen. Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge, MA: MIT Press. Haken, H., Kelso, J. A., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biological Cybernetics, 51, 347-356. Nam, H., (2007). Syllable-level intergestural timing model: Split-gesture dynamics focusing on positional asymmetry and moraic structure. In: Cole, J., Hualde, I. J. (Eds.), Laboratory Phonology 9. Mouton de Gruyter, New York, pp. 483–506. Nam, H. & Saltzman, E. (2003). A competitive, coupled oscillator of syllable structure. Proceedings of the XIIth International Congress of Phonetic Sciences 3: 2253-2256. Nava, E. (2010). Connecting Phrasal and Rhythmic Events: Evidence from Second Language Speech. PhD Dissertation. University of Southern California. Saltzman, E., Nam, H., Krivokapic, J., & Goldstein, L. (2008). A task-dynamic toolkit for modeling the effects of prosodic structure on articulation. In P. A. Barbosa, S. Madureira, & Reis,  C. (Eds.), Proceedings of the 4th International Conference on Speech Prosody (Speech Prosody 2008), Campinas, Brazil. Tuller, B., Case, P., Ding, M., & Kelso, J. A. S. (1994). The nonlinear dynamics of speech categorization. Journal of Experimental Psychology, 20, 3–16. Turvey, M., 1990. Coordination. Am. Psychologist 45, 938–953.