Strong anticipation: complexity matching in interpersonal coordination.

A subtle coordination occurs within complex systems, between multiple nested sub-systems. This intra-system coordination can be detected by the presence of 1/f fluctuations produced by the system. But coordination can occur also between systems. Interpersonal coordination has been studied from a local point of view until now, focusing on macroscopic interactions. But the recent concept of strong anticipation introduced by Dubois (Lect Notes Comput Sci 2684:110-132, 2003) suggests that interactions could occur on multiple levels between complex systems. The hypothesis is that time series in interpersonal synchronization present a matching of the complexity index (fractal exponent). Moreover, it is argued that this matching is not a consequence of short-term adaptations but reveals a global coordination between participants. Eleven pairs of participants oscillated a hand-held pendulum in the in-phase pattern for 11 min, in three conditions where the coupling strength was manipulated by the perceptual feedbacks. The results show a high correlation between fractal exponents irrespective of the coupling strength, and a very low percentage of local cross-correlations between time series appear at lag 0 and lag 1. These results suggest that interpersonal coordination, and more globally synchronization of participants with natural environments, is based on non-local time scales.