Numerical magnitude affects the perception of time and intensity

Abstract

The relative magnitude of an event (number magnitude) can have direct implications on timing judgments. Previous studies have found that large magnitude numbers are perceived to have longer durations than those of smaller numbers. This bias can be accounted for in several ways; first, the internal clock model theorizes that stimulus magnitude directly interacts with the components of a dedicated cognitive timer by increasing pacemaker speed. Another explanation posits that different quantitative dimensions (space, time, size, intensity and number) are all represented within a common cortical metric thus facilitating interactions within and across dimensions. I have expanded on this framework by proposing that perceived duration is inferred using flexibly applied rules of thumbs (heuristics) in which information from a more accessible dimension (e.g., number magnitude) is substituted for duration. Three paradigms were used to test this theory. First, commonalities in how the intervals separating discrete stimuli of different magnitudes were judged was examined across a variety of quantitative dimensions (number, size, and colour saturation). Perceived duration judgments increased systematically as the magnitude difference between the stimuli increased. This finding was robust against manipulations to sequence direction, and order, suggesting that interval duration was estimated by substituting information regarding the absolute magnitude difference. Second, the impact of number magnitude on sound intensity judgments was examined. When target sounds were presented simultaneously with large digits, they were categorized as loud more frequently, suggesting that participants substituted number magnitude when performing difficult sound intensity judgments in a manner similar to when judging duration. Third, the repetition of magnitude information presented in either symbolic (Arabic digits) or non symbolic (numerosities) formats was manipulated prior to the presentation of a target number, whose duration was judged. The results demonstrated that large numbers were judged to last for longer durations relative to small numbers. Furthermore, context had an effect in which a greater discrepancy in the target’s numerical magnitude from the initial context sequence resulted in a longer perceived duration. The results across all three paradigms suggest that people generally employ information regarding one magnitude dimension (number) when making difficult perceptual decisions in a related dimension (time, sound intensity).