Abstract-Two theories of timing, scalar expectancy theory (SET) and learning to time (LeT) During the past 15 years or so, the study of how animals time events has been guided to a large extent by two competing theories, the scalar expectancy theory (SET; Gibbon, 1977Gibbon, , 1991 and the behavioral theory of timing (BeT; Killeen & Fetterman, 1988). The present study reports the results of an experiment for which these two theories make substantially different predictions. However, instead of focusing on BeT directly, we focus on a more detailed version of BeT, a model called learning to time (LeT;Machado, 1997;Machado & Cevik, 1998). In what follows, we summarize the major attributes of SET and LeT, derive their predictions for a specific timing task, and then report the corresponding experimental findings.SET postulates an internal clock whose structure is represented in the left panel of Figure 1: A pacemaker generates pulses at a high rate; an accumulator counts the pulses emitted during the interval to be timed; and a long-term store saves the count obtained at the end of each trial. Because the rate of the pacemaker is assumed to vary across trials, the counts stored in memory will also vary. To time an event, the animal samples a number from its long-term memory at the beginning of the event and then compares continuously the sampled number with the number currently in the accumulator. The ratio between the two numbers controls the instrumental response.LeT, in contrast, consists of three major components (see the right panel of Fig. 1): a serial organization of behavioral states, a vector of associative links connecting the behavioral states to the instrumental response, and the instrumental response itself. At the onset of the event to be timed, only the first state is active, but as time elapses, the activation of each state flows to the next state in the series. How fast the activation spreads across states varies directly with the overall reinforcement rate in the situation. Each behavioral state is also coupled with the instrumental response, and the degree of the coupling changes in real time, decreasing during extinction and increasing during reinforcement. Thus, states that are strongly active during extinction will lose their coupling and eventually may not support the instrumental response, whereas states strongly active during reinforcement will increase their coupling and may therefore sustain the response. To paraphrase Hodgson, as quoted in James (1892/1985, p. 150), the behavioral states are the measuring tape, and reinforcement is the dividing engine that stamps its length. Finally, the strength of the instrumental response is obtained by adding the coupling values of the states, each value weighted by the activation of the corresponding state.Consider now the following temporal discrimination task and how each model conceptualizes what an animal exposed to it learns. A pigeon is presented with one of two signals, for example, a short-or a long-duration light. To obtain food, the anima...
