The extended body: a case study in the neurophenomenology of social interaction

Abstract

There is a growing realization in cognitive science that a theory of embodied intersubjectivity is needed to better account for social cognition. We highlight some challenges that must be addressed by attempts to interpret ‘simulation theory’ in terms of embodiment, and argue for an alternative approach that integrates phenomenology and dynamical systems theory in a mutually informing manner. Instead of ‘simulation’ we put forward the concept of the ‘extended body’, an enactive and phenomenological notion that emphasizes the socially mediated nature of embodiment. To illustrate the explanatory potential of this approach, we replicate an agent-based model of embodied social interaction. An analysis of the model demonstrates that the extended body can be explained in terms of mutual dynamical entanglement: inter-bodily resonance between individuals can give rise to self-sustaining interaction patterns that go beyond the behavioral capacities of isolated individuals by modulating their intra-bodily conditions of behavior generation.

Appendices

Appendix 1: Additional modeling details

The standard format of the continuous-time recurrent neural network (CTRNN) equations is as follows:

$$ \matrix{{*{20}{c}} {{\tau_i}{{\dot{y}}_i} = - {y_i} + \sum\limits_{{j = 1}}^N {{w_{{ji}}}\sigma \left( {{y_j} + {\theta_j}} \right) + {m_i}I} \quad i = 1, \ldots, N} \\ {\sigma (x) = \frac{1}{{\left( {1 + {e^{{ - x}}}} \right)}} } \\ } $$

Following Beer (1995, 2003), the form of these equations can be interpreted in a rough analogy to aspects of a functioning neuron, where y _i is the state of the average membrane potential of the ith neuron, y _i denotes the rate of change of this state, τ _i is the neuron’s membrane time constant, w _ji is the strength of the connection from the jth to the ith neuron, and θ _i is a bias term. The short-term average firing rate of the ith neuron is given by the output of the standard logistic activation function σ _i . Note, however, that this is only one possible interpretation of these equations, and it may be better to just think of them as describing a network of arbitrary dynamical components. The state of the input parameter I is equal to the state of the contact sensor (i.e. 0 for a lack of bodily contact, and 1 for the presence of bodily contact), where m _i is the magnitude of that state. Since the environment holds nothing but the two agents, the input I will always be equal for the two agents (either there is mutual overlapping or there is not).

On the basis of the output of the two functions σ ₂ and σ ₃ (range [0, 1] mapped into range [−1, 1]) we determine an agent’s movement in the one-dimensional space. Rightward and leftward movements are modeled as an increase and decrease of position in 1D space, respectively. The total change of position (velocity) is taken to be the difference between the respective contributions of the two dynamical components, and the contribution of each component v _i is calculated by adding to its output σ _i a stochastic element Noise _i , i.e. small random number drawn from a Gaussian distribution [mean = 0, variance = 0.05], and then scaling the result by an output gain g _i .

$$ \begin{array}{*{20}c} {v_{i} = g_{i} {\left( {\sigma _{i} + Noise_{i} } \right)}} \\ {velocities = \left\{ {\begin{array}{*{20}c} {v_{3} - v_{2} ,}{Agent\;A} \\ {v_{2} - v_{3} ,}{Agent\;B} \\ \end{array} } \right.} \\ \end{array} $$

The noise term introduces a small element of uncertainty into the model, such that the agents cannot rely on a direct mapping between their ‘expected’ change in position and their actual change in position. In contrast to the original work by Froese and Di Paolo (2008) we did not introduce sensor noise. Note that the total velocity of each agent is calculated slightly differently, with the two components v ₂ and v ₃ having the opposite sign. This represents the fact that the agents face each other in the one-dimensional environment, and their directions of movement are accordingly reversed.

Details of the evolutionary algorithm that was used in order to optimize the configuration of the CTRNNs can be found in Froese and Di Paolo (2008). Essentially, the probability of a particular configuration being chosen for the next round of optimization was set to be proportional to the agents’ ability to maximize the distance traveled together. This ability was objectively measured in terms of the distance traveled from their point of origin (the agents start at a random location within range [−25, 25] of each other) to their last point of contact before the end of the trial (after 50 units of time). The optimization process was terminated as soon as a configuration was found that enabled the agents to consistently coordinate their movements over a variety of initial conditions. Note that for the current study we did not repeat this optimization procedure, but simply took the particular configuration that was found by Froese and Di Paolo as our starting point.¹⁴ While this configuration is not the only way to solve the coordination task, it serves as a fitting proof of concept.

Appendix 2: Additional behavioral analysis

This Appendix provides a more detailed assessment of the behavioral interaction of the agents. The time series tracing the change of position of the agents over time (Fig. 4, top row) enables us to observe at least three characteristic features of the interaction.

First, the interaction process can be divided into two phases. During the first 500 hundred time steps the agents move apart and closer again with a decreasing magnitude of oscillation. The future direction is already discernable as a bias in the initial oscillations (but it can always still be affected by noise). When the agents settle on a preferred distance from each other, which happens to be just at the margin of making contact, the oscillations continue with reduced magnitude and the shared velocity is increased. At this point the second phase starts; the direction of the interaction pattern for the remainder of the trial has been established.

Second, the agents appear to exhibit an example of ‘active perception’. The informational value of the contact sensor in itself is very limited; it only provides a single binary signal (on/off). Accordingly, prolonged contact is not beneficial because it makes it uncertain to what extent the agents are actually overlapping, and prolonged absence of contact makes it uncertain how far they have drifted apart. By maintaining only a transient, oscillatory contact at the margin of the sensor boundary, the agents therefore ensure that the sensor signal provides accurate information about the relative position of the agents.

Third, it turns out that the relative position between the agents is always the same in the second phase of a trial, no matter whether they eventually end up moving leftwards or rightwards. This has the effect of decreasing the complexity of the task by turning four distinct possibilities (i.e. two types of relative position and two types of direction) into two possibilities (two types of direction). It also further enhances the informational value of the contact sensor, because while coupling could take place at one of two sides of the body (depending on relative position), it now is practically arranged to always take place at one and the same side only. Nevertheless, the task still remains nontrivial: a loss of contact has two different implications depending on context: in one case reestablishing contact requires a decrease of velocity in the shared direction (a ‘leader’ has to fall back), while in the other it requires an increase of velocity in the shared direction (a ‘follower’ has to catch up). In other words, the coordination of a common direction of movement is also about converging on complementary roles, of who will lead and who will follow.

Further behavioral investigations have revealed the following results. If the design of the playback condition is modeled more closely on the one originally used by Murray and Trevarthen, namely that recording of behavior only starts after the interaction has already been established and the playback is then started in the middle of the trial, we find that the interaction process still ends up breaking down. However, it only breaks down if the noise level was set to a value higher than 0, otherwise the live agent manages to maintain its behavior in the absence of the other’s responsiveness. At first sight this seems to be the same result as when we start playback from the beginning of the whole trial with 0 noise (see Fig. 5), but this is not the case. The data shown for the whole trial playback condition was derived by setting the internal activation state of the live agent to be the same it had during the normal condition. The middle of trial playback condition, on the other hand, does not reset the agent’s activation state to the same state it was in when the recording started. Interestingly, when the whole trial playback condition is started with 0 noise, but this time with newly randomized initial conditions for the live agent, then no interaction process is established.

The upshot of these results is that the role of the contingent responsiveness of the other agent changes during the progression of the trial. During the beginning of the trial the responsiveness is needed in order to coordinate the internal activation state of the agents. This makes sense because the agents need to converge on one or the other direction. After this initial coordination has taken place, the responsiveness of the other is needed to ensure that any discrepancies in coordinated movement that arise due to external perturbations do not accumulate over time to an unmanageable extent. Both of these roles of the other’s responsiveness modify the conditions in which the behaviors of the agents are generated. But while joint noise regulation pertains to conditions of the environment, the coordination of internal activation states during the initial moments of a trial pertains to conditions involving the agents themselves. We are particularly interested in the latter case because the notion of the extended body posits that inter-bodily resonance can transform the internal milieu of the agents. Our dynamical analysis is therefore focused on events occurring in the initial stages of the trials only.

Appendix 3: Additional dynamical analysis

For a strong notion of the extended body, it is not sufficient that the agents have the capacity for causing a switch in each other’s internal organization. This switch can be achieved by any kind of contact, in principle even by contact with non-agent objects that happen to cross the sensor. The idea of the extended body, on the other hand, requires that internal re-organization and mutual responsiveness are co-dependent factors, and that both of them are needed to establish coordinated movement. To put it differently, we are interested in (inter-bodily) socially contingent (intra-bodily) re-organization. In order to determine whether this is indeed the case in our model we must take a closer look at how an agent’s activation changes during its ongoing interaction with the other agent. Figure 8 illustrates how the inter-bodily interaction process relates to the intra-bodily switching between the two possible flow structures and their divergent equilibrium points.

The zigzag pattern noticeable in all of the graphs in Fig. 8 stems from the repeated on-off switching of the contact sensor during the interaction between the agents. Depending on the sensor status, only one or the other of the equilibrium points is actually present and is attracting the state’s trajectory. We can observe a ratchet effect that prevents the agents’ state from merely oscillating between the same two locations. This is due to the specific flow structure of the equilibrium points’ basins of attraction, which attracts the state in a nonlinear fashion (see Fig. 7). Note that when the interaction breaks down during the playback condition, the contact sensor remains off, the zigzag pattern disappears, and the agents’ state finally settles into the attractor that is defined by input I = 0.

As we know from Fig. 7 already, when the agents are on their own, i.e. without any change in input, the agents are fixed by the flow structure determined by I = 0, which is defined by a single equilibrium point, and which limits their behavior to movement in the same direction at a constant speed. What Fig. 8 reveals is that the robustness of the agents’ behavior, as demonstrated by their resilience to external perturbations (Fig. 5), depends on their internal state following a transient pattern within a far-from-equilibrium region of state space. In this transient region the agent’s internal flow structure effectively operates as a stable quasi-periodic equilibrium, rather than as a fixed-point attractor, which in this case has the desirable effect of expanding the agent’s behavioral repertoire. Instead of being effectively limited to a single direction of movement, the agent can now move both left and right in a flexible manner due to the interactively stabilized transient region.

Importantly, while this transient region enables the kind of flexible behavior that is required for sustaining a responsive interaction, it is also the case that what enables an agent’s internal state to first enter into (and then to remain within) this region is precisely the responsive behavior between the agents. The agents must guide each other’s internal state into this transient region by switching each other’s internal flow structure in an appropriate manner. This finding confirms that we are indeed dealing with a model of an extended body: each of the agent’s intra-bodily dynamics is extended by the other agent’s intra-bodily dynamics by means of the inter-bodily dynamics of their interaction process.