Time Perception Models

This article focuses on signal detection and information-processing models for time perception. The pseudologistic model and the scalar timingmodel are presented as exemplars of these two classes of models. For bothmodels Weber’s law describes the relationship between variability in perceived time andmean perceived time, and a power function with an exponent close to 1.0 describes the relationship between mean perceived time and clock time. The application of the two models to the temporal bisection task is considered. Time perception is a distinct area of study with its own psychophysical methods designed for assessing the perceived duration of a temporal interval. There is now an extensive database to guide the development of models of time perception. Most timing models are firmly rooted in an internal clock. Internal clock models postulate a timing-specific mechanism which produces perceived temporal values that bear orderly relations to real time. This timing-specific mechanism, or internal clock, is an interval timer, rather than a periodic or oscillatory mechanism. A periodic clock, such as the kind responsible for circadian rhythms, is continuously running and self-sustaining. In contrast, interval clocks need to be initiated with a signal. Once started, the system goes to completion, comes to a rest on its own, and must be restarted. The first psychophysical models for time perception were proposed at about the same time by Creelman (1962) and Treisman (1963). Creelman (1962) introduced the signaldetection approach, which was continued by Allan and Kristofferson (1974). The most sophisticated signal detection model is Killeen et al.’s (1997) Pseudo-logistic model (PLM). The information processing approach was introduced by Treisman (1963) and continued by many others, including Eisler (1975), Thomas and Cantor (1978), and Zakay and Block (1994). The most developed of the informationprocessing models is Gibbon et al.’s (1984) Scalar timing (ST), which has been reformulated as a connectionist model by Church and Broadbent (1991). In direct contrast to information-processing models is Killeen and Fetterman’s (1988) behavioral theory of timing (BeT). Because signal-detection models and informationprocessing models have been applied to both human and nonhuman timing data, we shall focus on such models in this article, presenting ST and PLM as exemplars of these two classes of models. Specific versions of ST and PLM have been derived for a variety of timing tasks, such as time-left, temporal generalization, and temporal bisection. We shall examine ST and PLM in their application to temporal bisection. In the prototypic temporal bisection task (e.g., Allan and Gibbon, 1991), the subject is familiarized with a constant pair of referents, one short (S) and the other long (L). On probe trials, a temporal interval t, S t L, is presented, and the subject is required to indicate whether t is more similar to S(RS) or to L(Rl). Temporal bisection data are summarized as a psychometric function relating the proportion of long responses, P(RL), to probe duration t. The bisection point (T1/2) is the value of t at which RS and RL occur with equal frequency, P(RL) 1⁄4 0.5. One interpretation of T1/2 is that it is the point of subjective equality (PSE), identifying the perceived value of t that is midway between S and L. Empirically, it has been found that the location of T1/2 is influenced by the size of the L-to-S ratio (r) and by the spacing of the probes (see Allan, 1998). For r 2, T1/2 is around the geometric mean (GM) of the S and L referents, but moves toward their arithmetic mean (AM) as r increases. For r > 2, T1/2 for linearly spaced probes is greater than that for logarithmically spaced probes, with the probe spacing effect becoming negligible for r 2.