Abstract
Natural movements, including smooth pursuit, comply with the two-thirds power law, which holds that movement speed (S) depends on the radius of curvature (R) raised to the power 1-2/3 (de’Sperati & Viviani, 1997). We examined the effect of the predictability of the motion path on the compliance of smooth pursuit with the law. A target that moved at a constant speed along a V-shaped path whose turn angle (0-180 deg) was unpredictable (unmarked) or predictable (marked by a line) (VSS 2019; Experiment 1). The time of the turn was chosen randomly from three values (Experiment 2). Eye speed decreased over time, reaching a minimum ~50ms after the direction change for marked, and ~150 ms for unmarked paths. The radius of curvature was found by fitting a circumscribed circle to eye positions over a 67-192 ms interval ending 60 ms after the minimum speed. The start was chosen to equate distance traveled before and after minimum speed was reached. Minimum eye speeds (S) were well fit (p<10-41) by the power law: log S = log K + (1-β)log R. Estimates of β were lower and closer to 2/3 for more predictable paths: β=.63 for marked, .74 for unmarked paths in Experiment 1; .65 for late turns and marked paths, .82-.85 for early turns and unmarked paths in Experiment 2. Larger estimates of β are associated with shallower slopes, suggesting that unpredictability weakened the relationship between curvature and speed, while predictability increased the compliance with the two-thirds power law. Predictability has been assumed to benefit pursuit mainly by reducing latencies. Here we find that another benefit is to regulate the relationship between the geometry and kinematics in a way that makes pursuit more compatible with likely natural targets: the movements of living things.