Abstract
Although time perception is based on the internal representation of time, whether the subjective timeline is scaled linearly or logarithmically remains an open issue. Evidence from previous research is mixed: while the classical internal-clock model assumes a linear scale with scalar variability, there is evidence that logarithmic timing provides a better fit to behavioral data. A major challenge for investigating the nature of the internal scale is that the retrieval process required for time judgments may involve a remapping of the subjective time back to the objective scale, complicating any direct interpretation of behavioral findings. Here, we used a novel approach, requiring rapid intuitive ‘ensemble’ averaging of a whole set of time intervals, to probe the subjective timeline. Specifically, observers’ task was to average a series of successively presented, auditory or visual, intervals in the time range 300–1300 ms. Importantly, the intervals were taken from three sets of durations, which were distributed such that the arithmetic mean (from the linear scale) and the geometric mean (from the logarithmic scale) were clearly distinguishable. Consistently across the three sets and the two presentation modalities, our results revealed subjective averaging to be close to the geometric mean, indicative of a logarithmic timeline underlying time perception.
Highlights
Time perception is based on the internal representation of time, whether the subjective timeline is scaled linearly or logarithmically remains an open issue
The striatal beat-frequency model[6,9,10] assumes that time intervals are encoded in the oscillatory firing patterns of cortical neurons, with the length of an interval being discernible, for time judgments, by the similarity of an oscillatory pattern with patterns stored in memory
The result pattern was similar for the visual experiment (Fig. 4b), with Set 2 generating a larger mean than both Set 1 (t (14) = 3.13, p = 0.015, BF10 = 7.1 ) and Set 3 (t (14) = 4.04, p < 0.01, BF10 = 32.49 ), with no difference between the latter (t (14) = 1.15, p = 0.80, BF10 = 0.46 ). This pattern of point of subjective equality (PSE) (Set 2 > Set 1 = Set 3) is consistent with one of our predictions, namely, that the main averaging process for rendering perceptual summary statistics is based on the geometric mean, in both the visual and the auditory modality
Summary
Time perception is based on the internal representation of time, whether the subjective timeline is scaled linearly or logarithmically remains an open issue. The bisection point—that is, the point that is subjectively distant to the short and long time references—was often found to be close to the geometric mean[22,23] Such observations led to the earliest speculation that the subjective timeline might be logarithmic in nature: if time were coded linearly, the midpoint on the subjective scale should be equidistant from both (the short and long) references, yielding their arithmetic mean. One prime example is the central-tendency e ffect[27,28]: instead of being veridical, observed time judgments are often assimilated towards the center of the sampled durations (i.e., short durations are over- and long durations under-estimated) This makes a direct interpretation of the timeline difficult, if not impossible. Though, that the mean of the prior is dynamically updated across trials by integrating previous sampled intervals into the prior—which is why it may not provide the best anchor for probing the internal timeline
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