Sayres Law See Murphys Laws

SCALAR TIMING THEORY. = scalar expectancy theory. Scalar timing theory is the most completely developed general quantitative model of animal timing today. It attempts to achieve the following four goals of timing/ temporal search: to account for data from human timing experiments as well as for animal timing experiments; to account for data from perceptual experiments ("time estimation"); to account for timing behavior not only in the range of seconds to minutes, but also for shorter and longer durations; and to account for inter-event distributions as well as to fixed time from some event until reinforcement. Three versions of timing theories, along with their hypothetical constructs, include: scalar timing theory (pulses from an "oscillator" are summed in an "accumulator" and stored in a distribution device); behavioral theory of timing (pulses from an "oscillator" advance behavioral states, each of which has some strength); and multiple oscillator model (half-phases from "multiple oscillators" are stored in an "autoassociation matrix"). Scalar timing theory has been categorized, also, into information-processing theories and connectionist theories. The notion of an "internal clock" of timing behavior is considered by many re searchers to be an information processing system/model that contains a number of components such as a "pacemaker," a switch that may connect the pacemaker to an "accumulator," a working (short-term) memory, and a reference (long-term) memory. According to this view, the rate of the pacemaker is not tied to the rate of reinforcement (as it is in the behavioral theory of timing), although it may vary randomly between intervals that are being timed. The connectionist theories of timing were developed to determine whether an associationist theory of timing could account for the data that were explained by scalar timing theory. In terms of their "psychological modularity," the three timing theories may be considered to be quite similar; that is, they all have information-processing stages of perception, memory, and decisions; however, their "representations" of each of these stages are different. For instance, J. Crystal reports that a connectionist theory of time (based on data from rats' judgments of time intervals in a choice procedure) with "multiple oscillators" is preferred over the linear timing hypothesis of scalar timing theory. The unique strength of scalar timing theory is that it has explicit solutions for several experimental procedures, and has provided precise fits to mean functions and to correlation patterns between indexes of behavior. The notable strength of the behavioral theory of timing, on the other hand, is that it provides a parsimonious account of data with emphasis on observed behavior. The outstanding feature of the multiple oscillator model is that it provides qualitative fits to some aspects (such as "periodicities" and "systematic residuals") of timing behavior. It may be speculated (e.g., Church, 1997) that the next generation of timing theories will include the following features: standards for description and quantitative evaluation; integration of neurobiological evidence into the timing theories; modification of current theories and development of a new theory that deals more efficiently with the combined accounts of the perceptual representation of time, the nature of temporal memory, and decision processes. In another case (Weardon, 1999), it is suggested that the future tripartite division of scalar timing theory into "clock," "memory," and "decision processes" is a use ful general framework for studying timing, including issues related to its neurobiological basis. See also ASSOCIATIVE LEARNING IN ANIMALS, THEORIES OF; BEHAVIORAL THEORY OF TIMING; INFORMATION/INFORMATION-PROCESSING THEORIES; PSYCHOLOGICAL TIME, MODELS OF; TIME, THEORIES OF. REFERENCES

Gibbon, J. (1977). Scalar expectancy theory and Weber's law in animal timing. Psychological Review, 84, 279-325. Church, R. M., & Broadbent, H. (1991). A connectionist model of timing. In M. Commons & S. Grossberg (Eds.), Neural network models of conditioning and action. Hillsdale, NJ: Erlbaum. Gibbon, J. (1991). Origins of scalar timing.

Learning and Motivation, 22, 3-38. Gibbon, J., & Church, R. M. (1992). Comparison of variance and covariance patterns in parallel and serial theories of timing. Journal of the Experimental Analysis of Behavior, 57, 393406.

Church, R. M. (1997). Timing and temporal search. In C. M. Bradshaw & E. Szabadi (Eds.), Time and behavior: Psychological and neurobehavioral analyses. Amsterdam, Netherlands: North-Holland. Crystal, J. (1999). Systematic nonlinearities in the perception of temporal intervals. Journal of Experimental Psychology: Animal Behavior Processes, 25, 3-17.

Weardon, J. H. (1999). Exploring and developing scalar timing theory. Behavioral Processes (Special issue. Interval timing: Is there a clock?), 45, 3-21.

Church, R. M. (2003). A concise introduction to scalar timing theory. In W. H. Meck (Ed.), Functional and neural mechanisms of internal timing. Boca Raton, FL: CRC Press.

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