Learning to Time (LET) or Scalar Expectancy Theory (SET)? A Critical Test of Two Models of Timing

Abstract

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...

Pigeons group time intervals according to their relative duration

“…First, it is possible that the pigeons used their own behavior to mediate comparison choice. Machado and Keen (1999) trained pigeons on two temporal discriminations, one involving the discrimination between samples of 1 and 4 sec, the other, the discrimination between samples of 4 and 16 sec. They found that most of their pigeons began pecking the sample after it had been presented for more than 1 sec, but they stopped pecking after about 6 sec.…”

Altered time-perception performance in individuals with high schizotypy levels

“…In light of these possibilities, the exact nature of the underlying mechanisms and interactions between the SET components and the timing deficit in high UE scorers is clearly in need of further exploration. Alternatively, the Learning to Time theory (LeT) 11,52 argues that timing occurs in terms of a chain of behavioral states initiated by environmental stimuli, with each state holding associative links with available responses 11 . In terms of the present task, these associative links are argued to differ in strength between each behavioral state and the responses available (i.e., S and L), with earlier behavioral states in the chain more strongly linked to the "short" choice, whilst later behavioral states are more strongly linked to the L choice.…”

Prospective and retrospective timing by pigeons

“…The probe tests that we used were similar, but not identical, to probe tests given by Machado and Keen (1999 Both panels show that accuracy was higher under prospective cuing conditions (dark hatched bars) than under retrospective conditions (light stippled bars). This difference in cuing condition was consistent across all birds and test ranges except for Pigeon 52 in the long set.…”

“…The probe tests were similar, but not identical, to probe tests used by Machado and Keen (1999). In their procedure, the choice-key colors cuing the test range were a houselight and a white center-key light.…”

“…Under the dual-timing task, pigeons were cued about the test range by the color of a center-key light stimulus and choice-key light stimuli, all r of which were identical for a particular test range (red for the short range and green for the long range). This duald timing task is similar to a procedure used by Machado and Keen (1999), who also intermixed two test ranges within sessions using a temporal discrimination task. Their test ranges were 1 versus 4 sec and 4 versus 16 sec, with the test range cued by different choice-key colors.…”