Introduction

In 1971 John Gibbon wrote, as the first sentence of an article in the Journal of Mathematical Psychology, "Scalar timing is proposed as the basic latency mechanism underlying asymptotic free-operant avoidance performance." He described the avoidance latency as a time estimate, and proposed that "time estimates are scale transforms of a single stochastic process." In an influential review, Gibbon (1977) extended this analysis to the behavior of animals in many other timing procedures. The essence of scalar timing is the "scale transform" idea. That is, the pattern of responding in time is the same at all time intervals if time is scaled in relative units (proportion of the interval) rather than absolute units (such as seconds). A process model was developed as a mechanism that would produce quantitative fits of data from animal timing experiments (Gibbon and Church, 1984; Gibbon et al., 1984). With some additional assumptions, scalar timing theory has been extended to account for dynamic effects (acquisition, extinction, and transition effects) as well as mean response rate (Gallistel and Gibbon, 2000; Gallistel and Gibbon, 2002; Gibbon and Balsam, 1981).

This chapter is a tutorial on scalar timing theory. It presents the basic ideas of the theory, the relationship of these ideas to a formal model, and the use of the formal model for making quantitative predictions about data. In this chapter the predictions of the theory are based entirely on computer simulations rather than mathematical derivations. A specific example is given in which scalar timing theory is applied to a single measure of behavior obtained in a single type of procedure. Such simulations can be extended easily to many other procedures and other measures of behavior.

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