Perception of time in articulated visual events

Abstract

Perceived duration of a sensory event often exceeds its actual duration. This phenomenon is called time dilation. The distortion may occur because sensory systems are optimized for perception within their respective modalities and not for perception of time. We investigated how the dilation of visual events depends on the duration and content of events. Observers compared the durations of two successive visual stimuli while the luminance of one of the stimuli was modulated at different temporal frequencies. Time dilation correlated with the frequency of modulation and the duration of the stimulus: the faster the modulation and the longer the stimulus duration, the larger the dilation. Notably, time dilation was also accompanied by a decreased sensitivity to stimulus duration. We show that these results are consistent with the notion that stimulus duration is estimated using measurement intervals of the lengths that depend on stimulus frequency content. Estimation of temporal frequency content is more precise using longer measurement intervals, whereas estimation of temporal location is more precise using shorter ones. As a result, visual perception will benefit from using longer intervals when the stimulus is modulated so that its frequency content is measured more precisely. A side effect of using longer temporal intervals is a larger uncertainty about the timing of stimulus offset (temporal location), ensuing time dilation and the reduction of sensitivity to duration. Our findings support the view that time dilation follows from basic principles of measurement and from the notion that visual systems are optimized for visual perception rather than for perception of time.

Keywords: dilation; duration estimation; measurement; optimality; time perception; uncertainty principle; vision.

Figure 1

Results of Experiment 1. (A) Dilation increased as a function of both modulation frequency and standard duration. (B) Dilation increased more when S2 (the second stimulus) was modulated than when S1 was modulated: a manifestation of the time-order effect. (C) The effect of modulation frequency was larger for the higher frequency of modulation. Error bars represent 95% confidence intervals around the mean.

Figure 2

Results of Experiment 2: psychometric functions. The data are plotted separately for standard durations of 500 ms (A) and 1100 ms (B). The red squares and blue circles represent the conditions of luminance modulation present and absent, respectively. The data are averaged across observers. The curves are the cumulative normal fits to fractions of reports that the comparison stimuli appeared to be longer than the standard stimuli. The psychometric functions for 7 Hz modulation are shifted to the right relative to those with modulation absent, which is a manifestation of time dilation. Error bars represent 95% confidence intervals around the means.

Figure 3

Results of Experiment 2: bias and sensitivity. (A) Results of the analysis of decision criterion. Negative values of the criterion indicate a bias toward S1, and positive values indicate a bias toward S2. When S1 was modulated, observers were more likely to report that S1 was the longest stimulus, and vice versa for S2. Criterion was also affected by stimulus order. Observers were likely to report that the second stimulus was longer than the first. (B) Results of the analysis of sensitivity. Sensitivity to duration was lower for modulated than non-modulated stimuli. Sensitivity also decreased when S2 was the standard stimulus, independent of stimulus modulation. The error bars represent 95% confidence intervals.

Figure 4

Results of Experiment 2: ROC analysis. The ROC curves are averaged across the six observers for two standard durations and two standard stimulus orders. (A,B) The curves are separated by the factor of stimulus modulation. Luminance modulation reduced sensitivity to stimulus duration. The data are shown separately for the standard durations of 500 ms (A) and 1100 ms (B). (C,D) The curves are separated by the factor of stimulus order. Sensitivity was higher for the first (S1) than the second stimulus, for both standard durations of 500 ms (C) and 1100 ms (D).

Figure 5

Model of duration measurement. Luminance of the stimulus (top) is integrated using a window whose duration w_i is a function of time and stimulus modulation. At stimulus onset, window length is w₁, which then increases toward length w₂ at stimulus offset (as explained in the main text). The onset and offset of model response are estimated at the half of the maximal value of model response (bottom). S and S_m are the durations of the stimulus and model response, respectively. Since stimulus offset is estimated using a longer window than stimulus onset, response to stimulus offset is delayed, causing an apparent increase of stimulus duration.

Figure 6

Results of numerical simulation. (A) The amount of dilation predicted by the model is increased by stimulus modulation and it grows with stimulus duration. (B) Dilation was larger when the second stimulus (S2) was modulated than when S1 was modulated. This effect increased with stimulus duration.