Entropy of Movement Outcome in Space-Time

Abstract

Information entropy of the joint spatial and temporal (space-time) probability of discrete movement outcome was investigated in two experiments as a function of different movement strategies (space-time, space, and time instructional emphases), task goals (point-aiming and target-aiming) and movement speed-accuracy constraints. The variance of the movement spatial and temporal errors was reduced by instructional emphasis on the respective spatial or temporal dimension, but increased on the other dimension. The space-time entropy was lower in targetaiming task than the point aiming task but did not differ between instructional emphases. However, the joint probabilistic measure of spatial and temporal entropy showed that spatial error is traded for timing error in tasks with space-time criteria and that the pattern of movement error depends on the dimension of the measurement process. The unified entropy measure of movement outcome in space-time reveals a new relation for the speed-accuracy.

Entropy of space–time outcome in a movement speed–accuracy task

“…It seems that the movement amplitude contributed more influence to movement outcome in the temporal dimension than to movement outcome in the spatial dimension. This finding suggests that movement temporal error is more easily influenced compared to the movement spatial error by the different space-time constraints and movement amplitudes (Hsieh et al, 2013;Lai et al, 2015).…”

“…It is anticipated that the movement variability in terms of a probabilistic two dimensional space-time approach would be different from the variability measured in the traditional single dimension distribution analysis of spatial or temporal error because it captures a unified index of the collective spatial and temporal uncertainty. Lai et al (2015) showed that joint space-time entropy was sensitive to different speed-accuracy manipulations but did not investigate the speed-accuracy function for joint space-time entropy.…”

“…The use of entropy (Cover & Thomas, 1991;Shannon, 1948) as a reflection of variability in the motor system has, however, not been applied broadly in the motor control domain and tended to focus on movement outcome error in a single dimension (Lai, Mayer-Kress, & Newell, 2006;Lai, Mayer-Kress, Sosnoff, & Newell, 2005). Lai, Hsieh, and Newell (2015) investigated an unified spatial and temporal error measurement of the probabilistic estimates of movement outcomes that can be implemented even though the units for assessing movement error in spatial and temporal error are different. The measure is an unified space-time entropy because it considers the joint probability structure of spatial and temporal movement error (Scott, 1992;Williams, 1997).…”

Force-Time Entropy of Isometric Impulse

“…Hsieh et al (2015) investigated a unified joint probabilistic entropy estimate of spatial and temporal movement error (Lai et al, 2015;Scott, 1992;Williams, 1997). The results showed a U-shaped joint entropy function under the movement space-time conditions (different spatial and temporal criteria) for all three movement amplitudes.…”

“…Information entropy is a candidate measure within the concept of information theory models of human information processing (Shannon & Weaver, 1949;Williams, 1997) and it is based on probabilities as a foundation to unify both force and time error of the movement speed and accuracy relation (Hsieh, Pacheco, & Newell, 2015;Lai, Hsieh, & Newell, 2015). An advantage of an information entropy measure is that it is based on the probability of the actual frequency distribution irrespective of the measured movement and force error dimensions and assumptions about a normal distribution.…”