Human odometer is gait-symmetry specific

Abstract

In 1709, Berkeley hypothesized of the human that distance is measurable by 'the motion of his body, which is perceivable by touch'. To be sufficiently general and reliable, Berkeley's hypothesis must imply that distance measured by legged locomotion approximates actual distance, with the measure invariant to gait, speed and number of steps. We studied blindfolded human participants in a task in which they travelled by legged locomotion from a fixed starting point A to a variable terminus B, and then reproduced, by legged locomotion from B, the A-B distance. The outbound ('measure') and return ('report') gait could be the same or different, with similar or dissimilar step sizes and step frequencies.In five experiments we manipulated bipedal gait according to the primary versus secondary distinction revealed in symmetry group analyses of locomotion patterns. Berkeley's hypothesis held only when the measure and report gaits were of the same symmetry class, indicating that idiothetic distance measurement is gait-symmetry specific. Results suggest that human odometry (and perhaps animal odometry more generally) entails variables that encompass the limbs in coordination, such as global phase, and not variables at the level of the single limb, such as step length and step number, as traditionally assumed.

Symmetry and order parameter dynamics of the human odometer

“…For experimental distances of 7.6, 15.2, and 22.9 m, Turvey et al (2009) confirmed Schwartz's (1999 finding that walk-walk and run-walk were equivalent M − R conditions (see also Isenhower et al 2012), but showed that it was a special case. They did so by manipulating the symmetry classes of bipedal gaits identified by Pinto and Golubitsky (2006).…”

“…In the laboratory, the measure M and the report R can both be conducted without benefit of vision. When so conducted, experiments (e.g., Isenhower et al 2012;Turvey et al 2009Turvey et al , 2012 suggest that M and R should be conceived as two components of a single system. Here we present an axiomatic basis for deriving the model of the M − R system developed heuristically in Turvey et al (2012).…”

“…In Gibson's (1966) classification of perceptual systems, the substrate variant of idiothetic information is detected by the haptic perceptual system and the inertial variant is detected by the basic orienting system (statocyst, vestibular organ). The substrate variant seems to be the more general basis for a non-visual ability to measure traveled distance (Etienne et al 1998), an ability common to humans (Isenhower et al 2012;Klatzky et al 1990;Mittelstaedt and Mittelstaedt 2001;Schwartz 1999;Turvey et al 2009), dogs (Séguinot et al 1998), fiddler crabs (Walls and Layne 2009), spiders (Barth 2004;Seyfarth and Barth 1972), and desert ants (Wittlinger et al 2006(Wittlinger et al , 2007Wohlgemuth et al 2001).…”

“…A primary bipedal gait (walk, run, slow two-footed hop, fast two-footed hop) is one for which the spatio-temporal symmetries satisfy the dihedral group D 2 (see Pinto and Golubitsky 2006;Pinto 2007;Turvey et al 2009Turvey et al , 2012. All three transpositions are entailed.…”

Challenges for the understanding of the dynamics of social coordination

“…This means that the same behaviors can be achieved adaptively by a family of systems of interacting components. Recently, based on the same classification approach, Turvey et al (2009) have shown that the way we measure distance by the use of our locomotor motion is determined by gait symmetry. Interestingly, Marey (1873) analyzed the coordination between two humans walking one closely following the other, and found that the single animal quadruped gaits are spontaneously adopted (see also Harrison and Richardson, 2009), hence the vast ensemble of group theoretic predictions for quadrupeds could be tested in a dyadic scheme in future experiments.…”