We measured the motion of the horse and the riders for a working trot, with the rider sitting on the saddle throughout. The two riders were instructed to perform a trot on different trials (N = 8) with the same horse, as if they were competing in a dressage competition. To analyze the movement of the horse and the rider, we recorded and digitized, respectively, a set of 10 and a set of 8 markers, the locations of which are shown in Figure 1A. We used the sagittal plane spanned by the horizontal (x) and vertical (z) axes of the laboratory frame of reference to represent the motion of the markers.

FIGURE 1 Time series of vertical displacement. A. Locations of the 18 markers on the bodies of the rider and the horse, recorded on the x–z plane (axes shown). B. Representative time series of the oscillations along the z coordinate. Top. Riders. Bottom. (more ...)

Obviously, the periodic nature of the motions plays an important role in the analysis and understanding of the coordination between the horse and rider as a coupled dynamical system. As can be seen in Figure 1B, the time series of the two bodies displayed fairly regular oscillatory movements along the vertical axis, particularly the head and the back of the horse and the entire body of the rider. Because the horse moves the rider up and down through translational motion, the rider must continually adjust his or her movements to accommodate the mechanical interaction with the horse—a kind of impedance matching (Hogan, 1985). The very nature of the task of riding is informationally linked to the horse’s locomotion through various points of contact, such as the saddle (bottom), the trunk (legs), the stirrups (feet), and the reins (hands). Note the essential reciprocity of those points of contact. For example, the horse’s gait may be altered subtly by the shape of the saddle (Fruewirth, Peham, & Scheidl, 2002; in equestrian circles they say a horse is sensitive enough to detect a fly on its back and good riding is “all about feel”). Observed oscillations in the movements of the horse and the riders can be directly related to the relative timing of the limbs in a characteristic trot; that is, one pair of diagonal legs moves in phase and half a period out of phase with the other diagonal pair (homologous limbs are antiphase). As a result, for each cycle of a given pair of diagonal legs, there are two vertical oscillations of the trunk, giving rise to a 2:1 frequency ratio (the so-called two-beat pattern; for comparison, walk and gallop are four beats and canter is three beats). Notice in Figure 1B that the vertical oscillations of the riders were of the same magnitude as the oscillations of the sacrum and the head of the horse. A closer look at the rider’s motions reveals that the joints from the shoulder to the wrist of the expert (Figure 1C, right time series) oscillated together in time. By contrast, the movements of the hobby rider (Figure 1C, left time series) exhibited a delay that traveled and appeared to grow from the shoulder to the wrist. That delay began at the lowest point of the cycle, which corresponded to the beginning of limb extension in the horse. As a result, the expert was able to keep the motion of all the joints of the upper body closely synchronized with the horse’s trunk, whereas for the novice, that synchrony was disrupted at each vertical extension of the horse.

To quantify the coordination between the horse and the rider, we calculated the mean and standard deviation of the relative phase (Batschelet, 1981) between a reference marker located on the sacrum of the horse and each marker on the rider (Figure 2). As shown in Figure 2A and B, the mean relative phase across the markers differed between the riders, F(1, 14) = 8.23, p < .05. In particular, the novice rider exhibited a larger phase lag relative to the horse’s sacrum than the expert did. But the interaction between the skill of the rider and the rider’s ensemble motions (given by the anatomical markers) was also significant, F(7, 98) = 52.95, p < .01. Whereas the expert’s shoulder, elbow, and wrist were aligned (the so-called straight-line position indicative of excellent balance), the novice’s motions displayed a systematic phase shift (cf. shaded regions in Figure 2A and B). Those mean changes in relative phase were accompanied by a consistent increase in relative phase variability, a measure that has been shown to index the stability of coordination (Kelso, 1984), F(7, 98) = 3.41 p < .01 (Figure 2C and D). The insets in Figure 2C and D show the distribution of the relative phases for the wrist marker for both riders and the corresponding power spectra for a representative trial. The sharper peak displayed by the expert (Figure 2D) suggests that strong phase synchronization is achieved only after extended practice and learning.

FIGURE 2 Mean and standard deviation of relative phase of the vertical oscillations of the rider with respect to the sacrum of the horse. A. Mean relative phase in degrees for the novice for all the markers and all the trials (n = 8). B. Mean relative phase for (more ...)

An inspection of the mean relative phase between the sacrum of the horse and sensors located on the lower body of the rider revealed additional differences between the riders. For the expert rider, the heel went up much later than the toe, whereas heel and toe moved more closely together in the novice (Figure 2A and B). Those rider-specific phasing patterns suggest that the expert used ankle flexion to damp vertical oscillations of the horse, whereas the novice kept her ankle joint still and stiff. Later activation of the heel relative to the toe may also allow the expert rider to grip the trunk of the horse better and more flexibly direct its motion. In equestrian jargon, the rider is taught to “sit deep” and “push everything down to the heel,” which is the key to driving the motion of the horse. Clearly, having flexibility at that local level allows the expert to maintain stable phase synchrony between his body and the horse, whereas the novice is more passively perturbed by the force of the horse’s vertical motion.

Differences in the global coordination between the riders are illustrated by the time series of the angle (θ) between the trunk of the rider and the vertical, which displays clearly more regular oscillations for the expert than the novice (Figure 3A and B). Whereas the expert sat deeper and absorbed the up–down motion of the horse, the novice sat straighter, likely tensing more through the trunk, and was subjected to the “bang-bang” jarring motion of the horse (Figure 3A). As a result, the expert’s motions flowed in time with the horse, whereas the novice lacked resonance with the horse and was unable to follow the two-beat pattern. Spectral analysis of θ bore out that observation: The expert displayed a single peak conforming to the up-and-down motion of the horse; the dominant peak for the novice was actually half that expressed by the horse (Figure 3C). Moreover, the between-trial variability of the mean and the standard deviation of θ were much smaller for the expert than for the novice (Figure 3D and E). The remarkable consistency of the expert in performing the two-beat pattern was nicely expressed by the autocorrelation function (cf. Figure 3F and G).

FIGURE 3 Time evolution of the angle formed by the trunk of the riders and the vertical. A–B. Time series of the angle θ formed by the trunk of the riders (approximated from the markers located at the hip and shoulder) and the vertical axis for (more ...)

To determine whether the horse was influenced by the rider, as indexed by the variability of the horse’s behavior, we separately extracted the periods between extensions and between flexions, corresponding, respectively, to minima and maxima of the vertical motion of the sacrum, and calculated the standard deviation of those periods for each trial. The time interval between extensions (but not flexions) of the horse was significantly less variable when it was ridden by the expert than when it was ridden by the hobby rider, t(14) = 2.85, p < .05, a result that is consistent with the fact that the novice’s movements were most perturbed during the extension phase (Figure 1). We found no dependence of the variability of the time interval between extensions and the frequency of vertical oscillation of the sacrum. The observed regularity of the movements of the horse is thus related to the skill of the rider and no doubt facilitates the phase synchronization between the rider and the horse.

The ensemble spatiotemporal stability of the rider~horse system¹ is clearly connected to the rider’s capacity to adapt to the motion of the horse (and vice versa), an ability that is acquired through extended learning and practice. An obvious candidate for such a mutual relation is the mechanical coupling between horse and rider. However, information exchange between the two is likely to play a key role, too. In particular, the horse and the rider share tactile information through points of contact at the saddle, rein, stirrups, and between the legs of the rider and the trunk of the horse. At those particular points, information pick-up is a function of the relative motions of the horse and the rider. Synchronization between the two likely enhances, and is enhanced by, haptic (i.e., active touch) information (Kelso, Fink, DeLaplain, & Carson, 2001). Evidence for more stable and precise synchronization in the skilled rider suggests enhanced ability to anticipate and use haptic information more effectively. Little is known, however, about how that skill actually develops.

Our findings show that the relative phase between horse and rider captures the overall spatiotemporal organization of the horse~rider system. The same variable has been found to capture the relative timing between limbs in animal gait patterns (Grillner, 1985; Rand et al., 1988; Schöner et al., 1990), between limbs and within limbs in human voluntary actions (Haken, Kelso, & Bunz, 1985; Kelso, 1984, 1995; Kelso, Buchanan, & Wallace, 1991; see Turvey, 1990, for a review), between sensory and motor systems (Kelso, Delcolle, & Schöner, 1990; Kelso et al., 2001), and between people (Schmidt, Carello, & Turvey, 1990). It is also a key coordination variable for neural circuits called central pattern generators (Grillner, 1985, 2003; Schöner & Kelso, 1988) and is portrayed as a candidate for the integration of brain rhythms and segregated brain areas (Gray, König, Engel, & Singer, 1989; Kelso et al., 1992; Palva, Palva, & Kaila, 2005; Varela, Lachaux, Rodriguez, & Martinerie, 2001). The reported phase synchronization between the horse and the rider clearly belongs to a family of processes generic to the organization of complex physical, chemical, and biological systems (Kelso, 1995; Kuramoto, 1984; Pikovsky, Rosemblum, & Kurths, 2001; Winfree, 1980). But, whereas phase synchronization is considered universal and spontaneous in weakly coupled oscillators, it is far from a given here: Our results showed that the coordination dynamics between two such vastly different brain~body systems as a horse and a rider requires practice and training. Stiff and tense movements must become fluid and flexible. Skill in this case requires sensitivity to and anticipation of the horse’s motion. It’s all about “feel,” and some people apparently never get it.

National Institute of Mental Health Grants MH 42900 and MH01386 and a U.S. Office of Naval Research grant supported this work. We thank JASK’s niece, Jacqueline McPherson (née Burns), a Bronze Medalist in the European Young Rider 3-day Event Championships at Burley, England, in 1983, for her advice and insightful comments. Two movies (mpeg format) of representative motions of the expert and novice riders and the horse can be obtained from the corresponding author.

J. Lagarde, Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton.

C. Peham, Clinic of Orthopedics in Ungulates, University of Veterinary Medicine Vienna, Wien, Austria.

T. Licka, Clinic of Orthopedics in Ungulates, University of Veterinary Medicine Vienna, Wien, Austria.

J. A. S. Kelso, Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton.