Allometric Scaling Laws for Temporal Proximity in Perceptual Organization

In both space and time, proximity plays an important role in the formation of perceived groups, objects, and scenes. Proximity is especially critical in the temporal domain where there are constraints-pauses or delays between neighboring events, that when of sufficient size, defeat the grouping processes that underlay temporal integration. A framework is developed where temporal proximity constraints are theorized to reflect lifetimes of exponential decay processes, and this identification leads to an inquiry into their scaling properties. In a study focusing on rhythmic pulse, the slowest tempo permitting stable rhythmic performance is shown to satisfy an allometry with a power-law exponent close to that of heart rate. The coefficient of variation, a measure of drumming stability and precision, is also shown to obey an allometry. A theory is developed that predicts that allometry in the coefficient of variation exists only at adagio and largo tempi. In a second experiment, this theory is tested by replicating the finding of precision allometry at 60 bpm, and by finding that precision is independent of body size at the marching tempo of 120 bpm. A third experiment examined proximity constraints in apparent motion, historically a defining example of temporal organization. Using a behavioral method for measuring path vividness, it is demonstrated that proximity constraints for the percept of illusory motion paths also satisfy an allometry. These two examples of proximity constraint scaling suggest that allometry may be a generic feature of temporal integration.