Everyday human actions often occur in a social context. Past psychological research has found that the motor behavior of socially situated individuals tends to be coordinated. Our research performed over the last 20 years has sought to understand how the mutuality, accommodation, and synchrony found in everyday interactional coordination can be understood using a dynamical theory of behavioral order, namely coordination dynamics. Using laboratory interpersonal tasks, we have demonstrated that when two people are asked to rhythmically coordinate their limbs they show behavioral phenomena identical to those found in bimanual interlimb coordination, which has been mathematically modeled as a dynamical process. Research has demonstrated that these same dynamical organizing principles can coordinate the rhythmic movements of two people unintentionally and that the weaker, intermittent coordination that ensues is affected by both perceptual (e.g., attentional focus and information pickup activity of the visual system) and dynamical constraints (e.g., intrapersonal rhythmic synergies and period basin of entrainment). Other research has investigated how traditional social and personality properties of a dyad (rapport, social competence) relate to dynamical properties of a dyad’s coordinated movements and how the stability of coordinated movements mirrors the stability of mental connectedness experienced in social interactions. 1 Dynamics of Interpersonal Coordination Psychological theory over the past few decades has had a growing appreciation that mind and knowing are embodied and that action not only reflects the mind (the cornerstone of all cognitive experiments) but is itself imbued with significance, that is, it is the vehicle by which we realize our mind, our thoughts, our values [12, 94]. There has also been for some time an appreciation that many natural actions are performed in a social context  and that social and physical environments are nested with their meanings existing side by side in natural perception and action . Simple actions such as reaching, locomotion, or even standing still are often performed to achieve a social goal and can then be socially defined as, for example, a caress, an escape or 282 R. C. Schmidt and M. J. Richardson opportunity for a conversation. Generic motor movements are nested within a higher-order definition of the actions that are defined intersubjectively in terms of another person, in terms of an interpersonal situation that generally occurs over a longer time scale than the motor gesture itself and is used to establish and maintain social relationships as well as achieve mutual action goals. But how does one begin to understand this social level of perception and action ? What are our expectations for how to understand the structure of such social behaviors? What taxonomies should we use to define the various kinds of embodied social interactions? One way is to define social actions in terms of cultural rituals as a cultural psychologist or social anthropologists would . Another way is define them in terms of different kinds of social relationships (dyads, strangers) or in terms of different kinds of social properties (gender, rapport) or personality characteristics (expressivity, dominance), from the perspective of a social psychologist [4, 59, 88]. But both of these domains, as important as they are, deal mainly with the ‘what’ rather than the ‘how’ of social actions. They focus on the ‘semantics’ rather than the ‘syntax’ of social interactions, the ‘content’ rather than the ‘process’. Focusing on the ‘process’ of social interactions, we notice two general kinds of social interactions. We all have had the pleasure of interpersonal interactions that have just ‘flowed’ : that effortless soccer goal or tennis match where you could just read others’ minds or that first date that you did not want to end. We also have been victims of untoward interpersonal events, from the mundane, like the awkward ‘dance’ two people do when they are trying to walk in the same space, to the more intimate, like ‘dates from hell’ and other failed personal interactions. We can characterize these positive and negative social interactions in terms of the efficiency and stability with which the component actions achieve an intended social goal. In order to understand this continuum of stabilities, the “how well it is going-ness”, that characterize these processes of social coordination, we need to turn to the universal logic of stability of natural systems: dynamical processes of self-organization. To understand the process of interpersonal interactions, we need to study the dynamics of interpersonal coordination. The research that we have performed over the past two decades has been dedicated to understanding the extent to which principles of coordination dynamics that govern intrapersonal movements can be used to understand the array of stabilities that arise in interpersonal coordination. In what follows, we will review this work with an eye toward how it is laying a foundation for a more general theory of social perception and action . 2 Universal Principles: Dances We Can and Cannot Do Haskins Labs in the 1980s was an exciting place to study the coordination and control of human movement. The theory of behavioral dynamics was being born and taking its first steps. Seminal theoretical papers written in the Dynamics of Interpersonal Coordination 283 early years of the decade by Kelso, Kugler, and Turvey [47, 51, 52] identified ideas empirically investigated in the later years of the decade. The ideas are as big now as they were 25 years ago. In order to answer how the many degrees of freedom of the perceptual-motor system are regulated, the traditional machine (i.e., neural or symbolic computational) theory answer was being replaced with a dynamical conception of order based on theories of physical biology. Neural wiring conceptions, such as the afference and efference distinction, were replaced by synergistic linkages between muscles that were dynamically constrained. Cognitive programs were replaced by equations of constraint that channel and guide a dynamic unfolding of behavior in a non-prescriptive manner. Key to empirically investigating how dynamics – namely “the free interplay of forces and mutual influences among components tending toward equilibrium or steady states  (pg. 6)” – organizes behavior was being able to conceive, model, and measure behavioral equilibrium or attractor states. While some researchers investigated the lawful nature of minimal energy states (comfort or optimal modes [53, 92]), Kelso and his students began to explore how the behavioral patterns associated with coordinated rhythmic limb movements can be modeled as representing the dynamics of periodic attractors or limit cycles . They further explored how the behavioral transitions between oscillatory phase modes (like in quadruped gait transitions) can be investigated in bimanual tasks [42, 43] and understood as phase transitions or bifurcations – a general nonlinear way that a dynamical system reorganizes itself after destabilization. In particular, the bimanual phenomenon was that the antiphase coordination of wrist or index fingers becomes increasingly less stable as the frequency of oscillation is increased, eventually breaking down and leading to a transition to inphase coordination. The dynamics of this behavioral switching was captured by a mathematical formalism that modeled both the steady state and phase transition behavior of coordinated rhythmic limb movements by capturing the dynamics of the relative phase angle (φ) between limbs : φ̇ = a sinφ− 2b sin 2φ+ √ Qζ. (1) In this equation (the HKB model), φ̇ is the rate of change of the relative phase angle formed between the two oscillators, a and b are coefficients whose magnitudes govern the strength of the between-oscillator coupling, and ζ is a Gaussian white noise process dictating a stochastic force of strength Q . Using the terminology of synergetics, φ is an order parameter (i.e., it summarizes the spatial temporal order of the rhythmic units) and the variables (e.g., frequency of oscillation) that influence its stability are control parameters [33, 34]. The bimanual phase mode switching phenomenon and model has had an inestimable impact on the dynamical theory of human movement because they provided a specific explication of behavioral attractors as well as how transitions occur between them. 284 R. C. Schmidt and M. J. Richardson This model of behavioral dynamics has generated an astounding amount of subsequent coordination research including our own on interpersonal coordination. The dynamics modeled in the phase transition phenomenon created a reorganization of behavioral order across the limbs of a single person. However, the question of the universality of these behavioral dynamics could be raised. If indeed, inphase and antiphase are canonical steady states that arise as a consequence of the dynamics of oscillators and their interactions, should not they also be differentially stable steady states in rhythmic movements coordinated across two people, across two neurally based oscillators linked by perceptual information ? Is it possible to have functional synergies or coordinative structures written across two individuals using the language of dynamics? In Schmidt, Carello, and Turvey , two seated participants were asked to visually coordinate their lower legs in either inphase or antiphase while oscillating them at a tempo of an auditory metronome pulse that increased in frequency from 0.6 to 2.0Hz by 0.2Hz increments every 5 s. In the first experiment, six pairs of undergraduate participants were instructed to keep and return to their original coordination phase mode if they fell out of it. The trials were videotaped and the relative phase angle between the legs of the participants was evaluated frame by frame. Of interest was the relative stability of the two modes of phasing and whether the likelihood of a breakdown in phase locking would grow as the frequency of oscillation was increased. Participants had a hard time maintaining the antiphase coordination of their lower legs at the higher frequencies. As seen in Fig. 1 (left), the variability at the higher frequencies for the antiphase mode is indicative of a breakdown Fig. 1. Data exhibiting the destabilization of relative phase with frequency increase in the interpersonal coordination of lower legs. Both relative phase variability and occurrences of the other phase modes are much greater for antiphase at higher frequencies. Adapted from  Dynamics of Interpersonal Coordination 285 in coordination, whereas this variability for inphase is large but still indicative of a stable state. Additionally, Fig. 1 (right) reveals the mean number of cycles that were in the ‘other’ phase mode was 1.5 times greater for antiphase than inphase for lower frequencies but nearly three times as great for higher frequencies of oscillation. A second experiment in this study analyzed the characteristics of the antiphase breakdown and transition to inphase using “do not intervene” participant instructions to allow the transition to naturally emerge. Results revealed that the transitions had the formal properties of a dynamical reorganization, namely divergence, critical fluctuations, and hysteresis . These visually coordinated interpersonal movements expressed the same differential dynamic stability of the intrapersonal phase modes modeled by Haken et al. , namely the inphase mode of interpersonal leg swinging is the globally stable behavioral attractor while the antiphase phase mode is a dynamically unstable local attractor. Scaling the oscillation frequency results in a gradual weakening of the local attractor, followed by a state of criticality (exhibited by increase in relaxation time and amplification of fluctuations), and then leads to a sudden annihilation of the local attractor and a switch to the globally attractive inphase mode (divergent response). A third experiment in this study verified that the critical nature of this phase transition is conditioned by the rate that the control parameter is increased . Increasing, the frequency plateau time (i.e., the length of time the relative phase was observed at each frequency) from 5 to 10 s resulted in an elimination of the state of criticality immediately before the transition because the observation time scale (plateau time = 10 s) was now equivalent to the random walk or first passage time required for such a transition to occur probabilistically due to chance [28, 29]. In summary, the three experiments of Schmidt et al.  demonstrated that the self-organizing coordination dynamics that Kelso observed in bimanual coordination of a single individual also occur in interpersonal coordination of movements. The between-person nature of these behavioral attractors demonstrated that the dynamical organizing principles of the HKB equation can operate in neurally based behavioral oscillatory systems that are coupled by perceptual information and, consequently, that these principles represent a universal self-organizing strategy that occurs at multiple scales of nature. 3 Frequency Detuning: The Firefly Dance An example of inter-organism dynamical synchronization that has been studied and modeled for some time is the mass coordination of firefly flashing in some parts of South East Asia [9, 87]. At dusk, male fireflies of certain species in New Guinea and Malaysia congregate in groups of hundreds or thousands in trees. As the night progresses, a synchronization of their flashing emerges resulting in a large, light-pulsing mass of fireflies. Synchronization has also been observed in certain North American fireflies; however, these species do 286 R. C. Schmidt and M. J. Richardson not congregate and their coupling is apparently weaker, yielding synchronization that is intermittent . Hanson  experimentally investigated and dynamically modeled the firefly synchronization process using an experimental method in which he manipulated the rate at which he periodically flashed a light at a firefly. The essential dynamical process in Hanson’s model of firefly entrainment is captured by an extension of the HKB equation  that contains a ∆ω term which specifies the eigenfrequency difference or frequency detuning between the two rhythmic units: φ̇ = ∆ω − a sinφ− 2b sin 2φ+ √ Qζ. (2) Entrainment of the fireflies in this model will occur (φ = 0) when the eigenfrequency difference between the firefly flashing and the experimental flashing of the light (∆ω) is small enough to be ‘balanced’ by the coordination ‘forces’ of the coupling function (−a sinφ − 2b sin 2φ). If the eigenfrequency difference is too large, φ̇ will be non-zero and absolute coordination  or phase locking will not occur and the firefly will not fully entrain to the light. The dynamical model also predicts that when the balancing of ∆ω and the coupling forces does occur and phase locking ensues, a phase lag between the two light flashes will emerge that is proportional in size to the ∆ω. Furthermore, the model predicts that when the flashing light is inherently faster, it should lead in the cycle, and when it is inherently slower, it should lag in the cycle. Because the phase lag demonstrates that the oscillating rhythmic unit (in this case, the firefly) is retaining some vestige of its original dynamic when in the coordinative state, von Holst referred to it as evidence of a ‘maintenance tendency’ of the oscillator . As seen in Fig. 2 (left), this increase in phase lag with an increase in frequency detuning is just what Hanson  found in his experiment. Importantly, these phase lag patternings of oscillators with different eigenfrequencies have been observed in a number of other examples of neurally based biological coordinations such as cockroach locomotion , the coordination of breathing and sucking in infants , and coordination of central pattern generators at the neural scale . Additionally, Turvey, Schmidt, and others [77, 85, 89] using an experimental paradigm developed by Kugler  at Haskins Labs have demonstrated that similar detuning patternings are seen in human bimanual coordination. This paradigm allows the manipulation of the detuning by having individuals bimanually swing (using ulnar-radial adduction) handheld pendulums whose lengths (and hence, whose frequencies) can be manipulated: Two pendulums of identical lengths will have a ∆ω of 0, whereas two pendulums of different lengths will have a non-zero ∆ω whose magnitude depends on the length difference. As reviewed in , the intrapersonal, bimanual relative phase patternings found using this wrist-pendulum paradigm beautifully support the predictions of the extended HKB model. But would the dynamical patterns of frequency detuning predicted by the HKB model and seen in fireflies, cockroaches, and undergraduate UConn Dynamics of Interpersonal Coordination 287 Fig. 2. The effect of frequency detuning (∆ω) on the relative phase lag in fireflies (left) and interpersonal coordination of wrist pendulums (right). Adapted from  and , respectively. Phase lag increases as the detuning becomes greater (i.e., as inherent frequencies become more different) as predicted by the extended HKB model students bimanually swinging wrist-pendulums also appear in interpersonal coordination of limbs? An initial study [68, 79] had two participants sitting side by side visually coordinate wrist-pendulum pairs that differed in their ∆ω’s. Participants could easily coordinate the pendulums in synchrony. But as Fig. 2 (right) depicts, as the length difference between the wrist-pendulums became greater, the phase lag between the pendulums increased such that the person with the shorter pendulum led in the cycle – just what is predicted by the dynamical model. Subsequent interpersonal wrist-pendulum studies investigated effects of phase mode and frequency of oscillation predicted by (2). Visual interpersonal wrist-pendulum coordination was found to be weaker as revealed by exaggerated relative phase lags and fluctuations (a) for antiphase compared to inphase and (b) for higher frequencies of oscillation compared to lower frequencies [2, 70]. These frequency detuning results verified that humans do indeed ‘dance’ like fireflies – human interpersonal rhythmic coordination is subject to the same dynamical laws as seen elsewhere in nature. They also demonstrate the explanatory power of the explicit modeling of the dynamical self-organizing processes captured by the HKB equation. 4 Coordination Dynamics in the Wild I: Unintentional Social Entrainment This early research on interpersonal coordination demonstrated that dynamics could constrain social actions in the laboratory during artificial tasks when people intend to coordinate. But do such processes of self-organization operate in circumstances where interpersonal coordination arises naturally in the 288 R. C. Schmidt and M. J. Richardson functional context of a social interaction? Social psychologists have been investigating naturalistic behavioral ‘entrainment’ processes in social interactions since the 1960’s (see  for a good review). For example, Condon and Ogston , who used film analysis (‘kinesics’) to investigate movement coordination interactions, state . . .analysis revealed harmonious or synchronous organizations of change between body motion and speech in both intra-individual and interactional behavior. Thus the body of the speaker dances in time with his speech. Further, the body of the listener dances in rhythm with that of the speaker (p. 338). Much social psychological research since that time has been directed at understanding what role this coordination of social behavior plays in human communication processes [7, 16, 50, 88]. Is it possible that the dynamical processes of self-organization captured by the HKB equation are the basis for the basic behavioral phenomenon of interactional synchrony? First pass evidence in support of this claim would be to demonstrate that these dynamical constraints operate even when people do not intend to coordinate. A series of studies we have performed demonstrated that they do. In the initial study , the visual wrist-pendulum task was modified to see whether such unintentional entrainment would occur. Participants were told that their task was to swing a pendulum at its comfort mode tempo, one that they could “swing all day”. During the first half of a trial, participant pairs were instructed to look straight ahead so that they could not see each other. During the second half of a trial, participants were told to look at the other participant’s moving pendulum but maintain their preferred tempo from the first half of the trial. Of interest was (a) whether in the second half of the trials when visual information was available the participants would tend to entrain their movements unintentionally and (b) whether the patterning of relative phase would be indicative of the HKB dynamic. In the first half of the trials, no phase entrainment was observed. The relative phase angle was not constant and all phase angles were equally observed in the coordination of the participants’ pendulums. This is not surprising because there was no perceptual coupling and ‘phase lapping’ occurred between the oscillations. In the second half of the trials when vision was available, the relative phase was also not constant and all phase angles were again observed but this time not equally: Relative phase angles near the attractor regions predicted by the HKB model (near 0 and 180◦) tended to dominate. The participants’ movements were weakly phase entrained. The coordination was not the absolute coordination (phase locking) exhibited in intentional visual coordination but rather relative coordination – a non-steady state coordination behavior produced by dynamical systems with weak attractor basins and intrinsic noise [46, 91, 96]. Such dynamical systems demonstrate the property of intermittency: A constant change in state with an attraction to certain regions of their underlying phase space. We saw further evidence for this by Dynamics of Interpersonal Coordination 289 measuring the rate of change of the relative phase angle (φ). In the first half of the trials, the average ∆φ calculated for nine 20◦ relative phase regions between 0 and 180◦ is large and shows no pattern. But in the second half of the trials when vision was available, the average ∆φ across the relative phase regions has an inverted u-shape (Fig. 3). The minimum rates of change near 0 and 180◦ suggests that the system was attracted to these regions. These results demonstrate that the dynamical principles of self-organization in the HKB model can constrain interpersonal coordination unintentionally, outside of participants’ awareness in a rather subtle fashion. Participants’ behavior was influenced by weak behavioral attractors, mere ‘ghosts’ of the attractors that we see constrain intentional coordination of rhythmic limb movements. Subsequent studies have verified this basic conclusion using progressively more naturalistic interaction circumstances. Note that neither components of the Schmidt and O’Brien task , neither just looking at another’s movements, nor swinging a wrist pendulum is a typical everyday task. To remedy the first concern, Richardson et al.  used a dyadic problem-solving task as a foil for investigating whether unintentional entrainment of pendulums would naturally occur. Cartoon faces were attached to the participants’ swinging pendulums (in the just looking and looking while talking conditions) or on stands on the side opposite of the other participant (in the no looking-no Fig. 3. The rate of change of relative phase (∆φ) at different relative phase regions without visual information (trial half 1) and with visual information (trial half 2). With vision available, ∆φ tends to decrease near 0 and 180◦ suggesting unintentional intermittent entrainment. Adapted from  290 R. C. Schmidt and M. J. Richardson talking control and not looking but talking conditions). Participants were told that the faces were placed on the pendulums in some conditions to make the dyadic problem-solving task more difficult to perform. In truth, they were put there so that participants would necessarily have visual information about each other’s movements during the problem-solving task. In each condition, a participant could only see one of the cartoon faces, and the dyad’s task was to determine together the differences (i.e., eye color, mouth shape) between the two faces. Debriefing verified that the participants indeed were unaware that the coordination of their pendulum swinging was the true purpose of the experiment. The results for the conditions in which visual information about the other person’s pendulum trajectory was available provided evidence similar to Schmidt and O’Brien  for unintentional entrainment as predicted by the HKB equation, that is, relative coordination, the intermittent attraction to inphase and antiphase relative phase angles, was observed. Another recent study  eliminated the artificiality of wrist-pendulum swinging by investigating the unintentional coordination of movements between two people rocking in rocking chairs. Participants were told that the experiment was investigating the ergonomics of rocking chair movements and that they were completing the task together because ‘testing two people at the same time was a more efficient way of collecting data’. In addition to investigating whether participants would unintentionally entrain their rocking movements, the experiments also manipulated the amount of visual information each participant had of each other’s rocking movements. To manipulate the information available, participants were also told that the study was investigating how different postural configurations affected the stability of rocking and that they would have to turn their head to focus on the red target that was located either on the arm rest of their partner’s chair, directly in front of them, or on the side away from their partner. These locations corresponded to the participants having focal, peripheral, or no information about their partner’s movements. As can be seen in Fig. 4, unintentional entrainment to Fig. 4. The distribution of relative phase angles between the rocking chair movements of co-participants as a function of the availability of visual information. More unintentional entrainment near inphase was found for the focal as compared to the peripheral information condition. Adapted from  Dynamics of Interpersonal Coordination 291 the inphase mode occurred and the degree of attraction to this mode was influence by the degree of information available – significantly less coordination was observed for the peripheral as compared to the focal information condition. The results of this and the preceding studies thus provide clear evidence that the dynamical processes of self-organization modeled by the HKB equation can constrain the unintentional synchrony in these laboratory tasks and are possibly responsible for the synchrony observed in ordinary, everyday social interactions. 5 The Expanded Interpersonal Synergy: Mediating Intrapersonal Rhythms In contrast to the coordination paradigms we have used which investigate the interpersonal synchronization of isolated limb movements, natural interpersonal interactions are whole body interactions with nested intrapersonal subtasks. Consider an ordinary interpersonal interaction: Two people have a conversation and walk together while carrying lunch trays in a cafeteria. The interpersonal coordination in their conversation and the interpersonal rhythmic synchrony of their leg movements occur along with other intrapersonally coordinated subtasks, in this case, carrying a tray and navigating through a cluttered environment. The orchestration of these subtasks needs to be coordinated within each person. Consequently, interpersonal interaction occurs in a context of ongoing intrapersonal coordination. Condon and Ogston  describe this intrapersonal coordination as being characterized by self-synchrony: . . .Behavior appears to be composed of flowing “configurations of change”, where body elements sustain and change movement together in an ordered fashion. It is this variable and serially-emerging pattern of sustaining and changing together which seems to constitute the “units” of behavior (p. 341). The idea is that these “configurations of change” define synchronization points for the various movements that we perform across the whole body. As we initiate arm movements to put down our lunch tray, we open our mouth to speak, lean our trunk forward, turn our head to turn right, and use our eyes to guide the tray to the table. In the next moment, we begin to lower our trunk to sit, turn our head toward our interactor to listen, and direct our gaze toward the salt shaker. Many parts of our body change and sustain direction at the same point in time and define the configuration of change for that moment. Condon and Ogsten  discussed as well the relation of this self-synchrony to interactional synchrony: Subject A, as he listens, displays a similar pattern of “configurations of change” which follows the same principle of change as those of Subject 292 R. C. Schmidt and M. J. Richardson B. Further, the “configurations of change” of Subject A are in precise synchrony with those of Subject B (p. 342). In more dynamical motor control terminology, we see that the interpersonal coordinative structure or synergy that self-organizes across two people in a naturalistic interaction has nested within it speech, bimanual, bipedal, and postural intrapersonal synergies that orchestrate the whole body movements of single individuals. Condon and Ogston’s point is that these intrapersonal synergies are coordinated – synchronized – in natural everyday actions and that their total functioning becomes synchronized across two people in interactions. Given this expanded, whole body view of coordination, the question that can be raised is how do the various intrapersonal synergies interact with or mediate the interpersonal entrainment that emerges in an interaction. We have investigated this question by looking at the role of eye movements and speech rhythms in interpersonal interactions. Our environmental interactions involve the active pickup of visual information that requires eye movements. This is especially true when perceiving animate objects whose movements need to be tracked in order to coordinate with them (e.g., getting on an escalator or entering an automatic revolving door). Much research has been performed investigating the constraints that movements of one effector have on the movements of another . However, because perceptual systems are typically conceived as static (in spite of the work of Gibson [26, 27] and Yarbus ), research has tended to ignore the constraints that movements of a visual system have on the coordination of effector movements that are occurring simultaneously. If one is tracking a moving object with one’s eyes, the question is whether these eye movements constrain the actions you make. Past research has noted a high degree of intrapersonal coordination between limb and saccade eye movements [37, 38, 90]. Given this intrapersonal synergy, we can ask whether a listener’s visual tracking of a speaker’s movements (e.g., gesticulation) mediates the interpersonal entrainment of the speaker and listener’s arm movements because the listener’s arm movements are intrapersonally coordinated with his/her tracking eye movements. Schmidt et al.  used an environmental entrainment paradigm to investigate the role of eye movements on unintentional entrainment. In this paradigm (Fig. 5, left), we were interested in whether participants would unintentionally entrain to a rhythmically moving stimulus. Participants were instructed to read aloud letters that randomly appeared on a projection screen while simultaneously swinging a wrist-pendulum. In addition to the letter stimuli, a sinusoidally oscillating stimulus moved horizontally across the screen. Participants were told that the purpose of the task was to measure the speed and accuracy of their reading and that their wrist movements and the oscillating stimulus were just motor and perceptual distracters. The real purpose of the experiment was to investigate whether participants would entrain their wrist movements to the oscillating stimulus and whether visual tracking the stimulus would facilitate this unintentional entrainment. We manipulated visual Dynamics of Interpersonal Coordination 293 Fig. 5. Environmental entrainment experimental setup used to study effects of visual tracking (left) and the distribution of relative phase angles between the visual stimulus and the participant’s wrist movements as a function of the visual tracking conditions (right). More unintentional entrainment near inphase was found for the tracking compared to the non-tracking condition. Adapted from  tracking by controlling where the letter to be read appeared. When the letters appeared in the center of the screen (above the oscillating stimulus), the participants were required to fix their gaze directly at the center of the screen (non-tracking condition). When the letters appeared on the visual stimulus, the participants needed to track the stimulus with their eyes as it oscillated from side to side in order to read the letters (tracking condition). To measure chance level coordination, trials were performed in which the letters appeared in the center of the screen along with an invisible oscillating stimulus (control condition). Results revealed that unintentional environmental entrainment between the wrist movements and the oscillating visual stimulus occurred. As seen in Fig. 5 (right), the results demonstrated that the visual tracking of the stimulus produced greater unintentional entrainment than the non-tracking condition. However, the non-tracking condition still exhibited some unintentional phase entrainment near 0 and 180◦. But does eye tracking facilitate the unintentional entrainment to the movements of another person as well as an oscillating dot? A follow-up study  investigated whether this result generalized to interpersonal rhythmic coordination by using the dyadic problem-solving paradigm of Richardson et al.  with tracking and non-tracking conditions. In the visual tracking condition, the cartoon pictures were attached to the end of the pendulums such that each participant had to visually track the motion of their co-actor’s movements in order to complete the dyadic task. In the non-tracking condition, the pictures were displayed on a floor stand positioned directly behind the motion of their co-actor’s pendulum; hence, no tracking movement of the eyes was required to 294 R. C. Schmidt and M. J. Richardson perform the problem-solving task. Results indicated that the wrist movements of the participants became more strongly entrained when visual tracking of their partner’s movements was required to complete the dyadic puzzle task. The results of both the environmental and interpersonal entrainment studies suggest that the dynamical, interpersonal ‘coordinative structure’ needs to be conceptualized as including the movements of two people coupled via an active, visual information pickup dynamic which is intrapersonally coupled to the individuals’ limbs. What we see is that the interaction of separate intrapersonal synergies (rhythmic wrist and eye tracking) constrains the creation of an interpersonal synergy. Future research needs to pay heed to the composite nature of the whole body system in studying environmental and interpersonal interactions and that a full understanding of the rhythmic synergy underlying interpersonal coordination involves understanding the intrapersonal coordination of motor and perceptual rhythms. Another behavior found in natural interpersonal interactions that needs to be intrapersonally coordinated with other body movements is speech. Speech often serves an explicit coordination function in social interactions . For example, the content of our speech dictates who does what in an interaction with a mutual social goal. (Perhaps most apparent when you are in a foreign country where you do not speak the language.) A more subtle question is whether the verbal information flow in a conversation is a sufficient informational medium to sustain interpersonal synchronization of bodily movements. If just looking at someone’s movements causes you to become entrained, will just talking to them also create interpersonal motor entrainment? Shockley et al.  investigated whether conversation is sufficient to entrain the postural sway of two interacting participants. Using a dyadic puzzle task not unlike that described above for Richardson et al. , participants interacted visually and verbally, interacted just verbally (faced opposite directions), interacted just visually (faced each other but conversed with an experimenter), or did not interact (control condition; faced away and conversed with an experimenter). The results demonstrated that postural entrainment occurred when participants were interacting verbally and that having visual information about the other person available by itself did not result in postural entrainment. Richardson et al.  using the interpersonal wrist-pendulum task ran similar verbal conditions (not looking but talking and looking while talking conditions; see above) to investigate whether such verbal information would affect interpersonal entrainment of rhythmic limb movements. They found that entrainment occurred for conditions where the participants could see each other but just chance level entrainment for the verbal information condition. An explanation for why interpersonal postural entrainment is affected by speech but limb entrainment is not has been suggested by a follow-up study. Using a similar method, Shockley et al.  found that verbal entrainment of posture does not occur on the basis of perceived speech signals but rather is dependent upon the rhythmic nature of the speech productions. That is, because speech rhythms of two people in conversation are coordinated and Dynamics of Interpersonal Coordination 295 these speech rhythms produce postural changes, the postural sway between the two interactors becomes coordinated. As with the eye-tracking studies above, it appears that the interpersonal synchronization of movements (limbs or posture) seems to be influenced by an interaction of intrapersonal rhythms (i.e., eye-wrist or speech posture). Why it is that the interpersonal entrainment of limb movements was not influenced by speech rhythms in Richardson et al.  needs to be understood as well. Studies of gesticulation have found evidence for intrapersonal synchronization of speech rhythms and hand movements , and other research has found that interpersonal gestural synchronization occurs in natural conversation although it depends heavily on the communicative and functional context of a gesture . It may be that the rhythms latent in the betweenperson conversation may have been too subtle to have any observable influence on the participants’ rhythmic limb movements in the Richardson et al.  study. There seems to have been a lack of intrapersonal ‘intimacy’ between the rhythms of a natural conversation and the sinusoidal rhythms of wristpendulum swinging. Accordingly, one may expect overtly rhythmic speech to provide a better functional context for finding a coupling between rhythmic limb movements and speech as well as speech-coordinated rhythmic limb movements between two people. We performed a recent study to address the first of these questions . Participants were required to read letters that appeared rhythmically in the middle of a computer screen while swinging a wrist-pendulum at a comfort mode tempo. Although the participants were told we were interested in their reading speed and accuracy, we were really measuring the degree of unintentional entrainment between the wrist-pendulum swinging and the rhythm of the appearing letters. This entrainment was evaluated under four speech conditions: out loud reading, silent reading (to test whether speech motor movements were necessary), no reading with a rhythmically appearing visual stimulus (to test whether purely visual rather than speech-mediated entrainment occurred), and no reading with no visual stimulus (control condition to test chance entrainment). The tempo of the appearing letters was also manipulated and presented at a period equal to the participant’s self-selected comfort mode tempo (determined in pretrials) or at a period that was slightly faster or slower than that tempo. Results provided evidence for both frequency and phase entrainment in the two reading conditions. The difference between the period of the wrist movements and the rhythmic stimulus (Fig. 6, left) decreased when either out loud or silent speech was performed, suggesting a ‘magnet effect’ . Additionally the relative phase distributions (Fig. 6, right) indicate a tendency to be at the front or back of the cycle (0◦ arbitrarily defined as the pendulum being away from the screen and 180◦ was defined as the pendulum being toward the screen) when the letter appeared in either the out loud or the silent speech conditions. These results provide evidence that speech rhythms can entrain limb rhythms. They also provide evidence that if the speech rhythm is synchronized 296 R. C. Schmidt and M. J. Richardson Fig. 6. Period difference (left) and distributions of relative phase angles between the letter-to-be-read stimulus and the participant’s wrist movements (right) for the different rhythmic speech conditions. The decrease in period difference for the reading conditions represents frequency entrainment (magnet effect), whereas the increase in relative phase occurrence near 0 and 180◦ represents phase entrainment between the wrist movements and the speech rhythm with an environmental rhythm, speech can mediate the entrainment of a limb rhythm and an environmental rhythm. Moreover, the silent reading results demonstrate that overt motor speech movements are not necessary for speech to play such a mediational role. More important seems to be the attentional rhythm  rather than the motor movements themselves. Such an explanation may have implications for why eye-tracking movements facilitate unintentional entrainment with an environmental rhythm. Future research needs to investigate whether the overt eye movements themselves are less important than the attentional attunement that the movements create. Regardless of this particular issue, the implication of this speech study is similar to that of the eye-tracking studies reviewed above: Intrapersonal rhythms and the synergies that create them are themselves coordinated and this self-synchrony can mediate the establishment of synchrony between people. 6 Informational and Dynamical Constraints on Unintentional Interpersonal Entrainment The research discussed thus far demonstrates that interpersonal entrainment emerges from dynamical laws operating via informational interactions. As much as unintentional interpersonal entrainment is a powerful effect, individual differences observed in our experiments suggest that it does not always occur. Such entrainment occurs only if certain conditions are fulfilled. Additional research we have performed has investigated more specifically the dynamical and informational constraints on unintentional interpersonal entrainment. Equation (2) suggests that the weak phase entrainment seen in the unintentional interpersonal coordination will occur as long as the difference in Dynamics of Interpersonal Coordination 297 inherent tempos of the oscillators (i.e., ∆ω) is not much larger than the coupling strength. This suggests that if two participants establish comfort mode tempos that are very different (i.e., create a large |∆ω| by virtue of ‘personal’ tempos), the coupling dynamic of (2) may not be strong enough to parry their respective ‘maintenance’ tendencies. Empirical results have supported this prediction. In the unintentional coordination experiment of Schmidt and O’Brien , ∆ω was manipulated by having participants swing pendulums of same or different lengths. A reduced concentration of relative phase angles around the attractors of 0 and 180◦ was found for conditions in which the participants swung pendulums of different lengths (i.e., different inherent frequencies) compared to conditions in which they swung pendulums of similar length. Furthermore, a reanalysis of the data of Richardson et al.  displayed in Fig. 7 suggests that even when participants have the same length pendulums, inherent differences in their selection of a comfort mode tempo will affect the likelihood of entrainment. This result raises not only the issue of what variables effect individual differences in comfort mode tempo (see ) but also the question of over what range of ∆ω’s unintentional visual entrainment will occur. This reanalysis suggests that there is a range of period differences over which interpersonal coordination will occur and that beyond this range the occurrence of unintentional coordination is highly unlikely. In other words, there appears to be a period basin of entrainment  for unintentional interpersonal coordination. In a recent study , we used the environmental coordination paradigm to measure this period basin for unintentional coordination to an environmental rhythm. Participants were Fig. 7. Cross-spectral coherence as a function of the difference in the natural (selfselected) period of participants’ wrist-pendulum movements. The natural period for each participant in a pair was calculated during no visual information control trials. Note that the coherence decreases as the period difference (naturally occurring ∆ω) increases, suggesting the existence of a period basin of entrainment 298 R. C. Schmidt and M. J. Richardson required to read letters presented on a sinusoidally oscillating visual stimulus while swinging a pendulum at a comfort mode tempo. This task was the same as the visual tracking condition of Schmidt et al.  discussed above in which we found unintentional entrainment in accord with the HKB dynamic. By initially determining the participant’s comfort mode tempo and then manipulating the period of the oscillating stimulus in approximately 25ms increments over a range 200 ms above and below the comfort mode tempo, we demonstrated that rhythmic limb movements become unintentionally entrained to the environmental rhythm when the period of the environmental rhythm was within ±150ms of the individual’s natural period. This range, estimated using entrainment to a non-person rhythm, is similar to that suggested by the interpersonal data in Fig. 7. A variable that may be related to the size of this basin is the amount of period variability exhibited by an individual. Because, as seen in Fig. 8, the magnitude of coherence between participants’ movements and the an oscillating visual stimulus mirrors the mean distribution of participants’ cycle-tocycle periods, we are currently investigating whether participant pairs with more overlap of their distributions of period (due to a sufficiently sized SD of period) will tend to have greater basins of entrainment and thus are more likely to become unintentionally entrained. An additional question concerns Fig. 8. The cross-spectral coherence between a participant’s wrist movements and an oscillating visual stimulus as a function of the difference between the participant’s natural period of movements and the stimulus period (solid line, black dots, bottom x-axis, left y-axis). Average period distribution of participants swinging a wrist pendulum for a 30-s trial (dashed line, white dots, top x-axis, right y-axis) Dynamics of Interpersonal Coordination 299 the constructive effect of movement variability or noise [14, 15, 65] on unintentional interpersonal coordination. Such noise-based enhancement reflects a process known as stochastic resonance, which occurs when the flow of information through a nonlinear system is maximized by the presence of sub-threshold noise . Thus, not only might an individual’s movement variability be a parametric constraint on visual entrainment, but it is also possible that such noise may operate to increase the stability of entrainment. We are currently investigating this possibility by using the environmental entrainment paradigm and adding different magnitudes of sub-threshold period variability (e.g., 0, 2, and 5% of the stimulus’ target period; see  for more details on this method) to the trajectory of the oscillating stimulus. Although participants are expected to become entrained to the visual stimulus when the stimulus is equal to the participant’s comfort tempo (no period difference) and contains no variability, more unintentional coordination is expected to be observed for the noisy stimulus when the stimulus’ period is less than or greater than the participant’s comfort tempo. That is, the basin of entrainment for unintentional coordination is expected to be extended for a ‘noisy’ stimulus compared to a no-noise stimulus. In addition to the dynamical constraints of naturally occurring differences in inherent tempos and noise, the stability of visual interpersonal coordination also depends on the availability and pickup of movement information. But what movement information needs to be detected for visual coordination to occur? Will any visual movement information do, or is some information more privileged or relevant for visual entrainment? Previous research on locomotion [55, 93] and rhythmic catching [1, 67] has demonstrated that the pickup of information during rhythmic tasks is not uniform and that the information available at certain discrete points may be more important for stable coordination. Consistent with these findings, Roerdink et al.  have demonstrated how individuals more often fix their gaze on the endpoints of an oscillating visual stimulus during a manually tracking task. Similarly, Byblow et al.  have found evidence to suggest that the endpoints of rhythmically moving limbs – namely the peak extension and flexion points – are the perceptual pickup points for bimanual coordination. A recent series of experiments conducted in our lab also suggests that the pickup of information at the endpoints of a movement is particularly important for visual coordination. In these experiments , participants were instructed to intentionally coordinate with an oscillating visual stimulus that had different phase regions (0◦/180◦, 90◦/270◦, 45◦/135◦) and phase amounts (80, 120, 160◦) of the stimulus’ trajectory occluded from view (Fig. 9, top left and bottom). Consistent with information at the endpoints being most important, an analysis of the entrainment variability (SDφ) revealed that occluding the endpoints (the phase regions at 0◦/180◦) resulted in significantly less stable wrist-stimulus coordination compared to when the middle phase 300 R. C. Schmidt and M. J. Richardson Fig. 9. Experimental setup and stimuli (left and bottom, respectively) used to study effects of visual occlusion (both location and amount) on intentional visual entrainment. Results (right) suggest that the variability of relative phase is only increased by occluding the ends (0◦/180◦) of the trajectory. Adapted from  regions (90◦/270◦ and 45◦/135◦) were occluded (Fig. 9, top right). When the middle phase regions were occluded, the stability of the coordination was the same as when none of the stimulus trajectory was occluded. Furthermore, the amount of phase occlusion was found to have no affect on the stability of the visual coordination. Although the above studies involved only a single individual coordinating with an environmental rhythm (stimulus), the findings can easily be generalized to interpersonal coordination, which is itself a form of environmental coordination (a co-actors movement is a type of environmental rhythm). Identifying the informational and dynamical constraints that influence the stability and emergence of unintentional coordination between people may provide perspective for understanding when and why social and interpersonal interactions succeed or break down. Dynamics of Interpersonal Coordination 301 7 Coordination Dynamics in the Wild II: Social–Psychological Variables In the interpersonal coordination studies reviewed above, we demonstrated how the stability of dyadic behavioral coordination is influenced by variables of action and perception – influenced by dynamical principles of motor synergies and their constituent variables (e.g., frequency of oscillation, detuning) as well as the kinematic structure of visual information and processes of information pickup and attentional attunement. But given that these action and perception processes occur naturally nested within a social context, one can ask how the stability of coordination dynamics is influenced by variables at the social–psychological scale. Social psychologists have been investigating this question in their studies of “interactional synchrony” in adults [5, 31, 41] as well as in infants [6, 19, 22, 39]. They have found that social variables such as attachment and rapport as well as psychological variables such as learning disabilities, mental illness, and expressivity constrain the degree of interactional synchrony observed in interactions. These investigations have involved naturalistic tasks where the interpersonal coordination is implicit within the interaction. The problem associated with such investigations is the difficulty of measuring the interactors’ movements and evaluating their coordination. Consequently, we have performed studies investigating the influence of social variables on interpersonal entrainment using more stereotypic perception and action tasks to circumvent these methodological problems as well as to allow us to study how social variables interact with the dynamics of interpersonal synergies. Schmidt et al.  used intentional antiphase wrist-pendulum coordination to investigate the effects of social competence on interpersonal coordination stability. The coordination task required participants to swing three pairs of pendulums whose length differences comprised three levels of detuning (∆ω = −0.32, 0, and 0.32) at two different tempos (slow: 0.65Hz and fast: 1.5Hz). Using a shortened version of the Riggio Social Skills Inventory , participants were selected to create homogeneous social competence dyads (both participants having high or both participants having low social competence) and heterogeneous dyads (one participant having high and the other having low competence). Socially competent people possess greater skill in social interactions, and are presumably more adept at perceiving the various possibilities for social action, perhaps by being more attuned to the facts of a situation and what types of actions they require . Consequently, an intuitive hypothesis for this investigation was that pairs with higher social competence would have more coordinated interactions. The social competence variable did affect the coordination dynamics but not as anticipated. The heterogeneous (High–Low) pairs demonstrated significantly fewer breakdowns in coordination than both the homogeneous (High– High and Low–Low) social competence pairs (High–High: 51%, Low–Low: 52%, High–Low: 86% phase-locked trials), indicating a stronger coordination 302 R. C. Schmidt and M. J. Richardson dynamic for the heterogeneous pairs. A marginal interaction between competence and frequency suggested that this result was primarily demonstrated for the faster tempos when coordination is generally less stable . Further more, for the trials that were phase-locked, only the High–High pairs did not show the typical phase lag relationship with the detuning variable ∆ω (i.e., the shorter pendulum leading in its cycle) that is predicted by (2). This result suggests that these High–High pairs did not use a dynamical strategy for ‘solving their coordination problem’. These outcomes can be rationalized by noting that the measure of social competence used correlated with a social control subscale. This correlation suggests that the type of competence characterizing the dyads was that of leadership or dominance. The results indicate that reciprocity (leader–follower) rather than symmetry (leader–leader or follower–follower) of this social competence facilitated the social coordination as well as the appropriating of a dynamical strategy to create the interpersonal coordination. This ‘control’ hypothesis leads one to expect that the high-competence individuals would be more likely to sustain a stronger maintenance tendency (i.e., a tendency to maintain their own preferred dynamic) than the low-competence individuals. Two results suggest that the high social competence individuals did have a stronger maintenance tendency when paired with a low-competence partner. First, the high-competence participants in these pairs led the low-competence participants in their cycles (by 2◦, albeit a non-significant difference), and second, the high-competence participants had lower fluctuations in their periods of oscillation than the low-competence participants (p < 0.05). Consequently, the results of this experiment seem to imply that (a) a person’s personality characteristics become embodied in their motor movements and, as a result, (b) these personality traits constrain the synchrony of their social interactions. The above study demonstrates that dispositional properties of individuals can affect the coordination dynamics assembled and these influences can be studied in laboratory experiments. But what about social circumstances? Will the kind of social task a pair of individuals performs affect their coordination dynamics as well? In a recent study performed with social psychologists Lucy Johnston of the University of Canterbury and Kerry Marsh of the University of Connecticut , we used the rocking chair unintentional coordination paradigm  and the dyadic problem-solving task  to study whether the dynamics of entrainment would reflect whether the participants performed a cooperative or a competitive dyadic task. A pair of participants sat in rocking chairs side by side. Cartoon faces were attached to their armrests such that each could only see one cartoon face – that of their partner’s. The participants’ task was to determine the differences between the two cartoon faces. However, this task was performed in one of two ways to make it either a competitive or a cooperative task: Participants were either jointly rewarded (cooperative condition) or individually rewarded (competitive condition) for the number of differences identified. After the task was performed, all participants were asked to rate how much they liked their partner and how pleasant they found Dynamics of Interpersonal Coordination 303 the interaction. Analysis of the results indicated that the cooperative pairs displayed more inphase coordination and marginally greater cross-spectral coherence than the competitive pairs, demonstrating an influence of the social goal on the coordination dynamics. Additionally, regression analyses found that the degrees of liking and perceived pleasantness of the interaction were each correlated with the cross-spectral coherence. These results suggest that the social circumstance in which individuals find themselves will constrain the degree of unintentional entrainment observed and that the stability of this interactional synchrony reflects the experience of psychological connectedness between the participants.