Bayesian estimation on logarithmic scales as an explanation for spatiotemporal interferences with a tendency of deceleration

Spatial and temporal information processing interfere with each other. Kappa effect is a famous spatiotemporal interference, in which the estimated time between two lights increases as an increase of distance between the lights, showing a tendency of deceleration. A classical model attributes the interference to constant speeds and predicts a linear relation, whereas a slowness model attributes the interference to slow speeds and proposes the tendency is the result of the variance of stimuli locations. The present study developed a logarithmic version of the classical model and asserts that the tendency is the result of the Web-Fechner law. These hypotheses were tested in two time discrimination tasks by manipulating the variance of stimuli locations and distance between stimuli. The results demonstrate that estimated time was not modulated by the variance of stimuli locations, and increased as an increase of distance with a tendency of deceleration. The Bayesian model on logarithmic scales made more accurate behavioral predictions than the linear model; the estimated constant speed of the logarithmic Bayesian model was equal to the absolute threshold of speed; the strength of the Kappa effect positively correlated with the variability of time perception. Findings suggest that the interference in the Kappa effect is driven by slow speeds, the strength of the interference is influenced by the variability of time perception, and the tendency of deceleration is the result of the Weber-Fechner law. This Bayesian framework may be useful when applied in the field of time perception and other types of cross-dimensional interferences.