## An Information Processing Metaphor of Scalar Timing Theory

The model consists of three processes: perception, memory, and decision (as illustrated in Figure 1.1). Perception of time consists of a pacemaker, a switch, and an accumulator. The pacemaker emits pulses according to some simple distribution. If a switch is closed, these pulses enter the accumulator, which can be reset by another switch. When reinforcement occurs, the number of pulses in the accumulator (transformed by a multiplicative constant) is stored in memory. Thus, memory consists of an increasing number of examples of times of reinforcement. The decision process is based on three inputs: the current time (from the accumulator), a remembered time of reinforcement (from a random sample of one element from memory), and a threshold (from a random sample of a distribution of thresholds). A ratio rule is used to determine whether to make a response.

Scalar timing theory is a process model in which there are an experimenter-determined input (the times of onset and termination of the stimuli, and the times of reinforcer delivery) and a subject-determined output (the response). The information-processing metaphor is clearly a cognitive theory with boxes and arrows; the boxes represent functional parts and the arrows represent rules of transformation. It involves multiple intervening variables. The input affects one or more intervening variables; each of the intervening variables affects other intervening variables or the output. The information-processing metaphor helps to organize the intervening variables and their interrelationships, but it is not an essential feature of the theory. Response

FIGURE 1.1 Information-processing metaphor of scalar timing theory.

Response

FIGURE 1.1 Information-processing metaphor of scalar timing theory.

### 1.2.3 A Formal Model of Scalar Timing Theory

The formal model consists of primitive terms (stimulus, reinforcer, and response) and quantitative transformation rules. It is not enough to write, "The pacemaker emits pulses according to some simple distribution." In order to make precise predictions, it is necessary to specify the distribution form and its parameters, such as mean and standard deviation. In scalar timing theory the distribution forms and some of the parameters are assumed, and other parameters are estimated from the data.

### 1.2.3.1 Pacemaker

Various assumptions have been made about the time series of pulses that are emitted by a pacemaker. These include the assumption of a fixed interpulse interval, a random (exponential) distribution of interpulse intervals, and a fixed interpulse interval during the timing of an interval, but a normal distribution of rates (Gibbon and Church, 1984). Because, at the durations used in most of the experimental research, other sources of scalar variability overwhelm the effects of pacemaker variability, any of these possibilities remains plausible (Gibbon, 1992).

### 1.2.3.2 Switch and Accumulator

The assumption is that a stimulus onset closes the switch and that pulses flow from the pacemaker to the accumulator when the switch is closed. The informal idea is that the switch starts the clock; i.e., it permits pulses to flow from the pacemaker into the accumulator. There is also the assumption that there is some latency between the occurrence of the stimulus and the closure of the switch; thus, there is some latency between the physical stimulus and the starting of the clock. This is assumed to be a normally distributed variable with some mean and standard deviation, t1 = n(|t1, ot1). Similarly, at the end of a stimulus the switch opens with some latency, t2 = °t2). Thus, the duration of switch closure (and the length of time that pulses are flowing into the accumulator) is t2 - tj. The value in the accumulator is one of three inputs to a decision. The other two are the memory and the threshold.

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### Responses

• peony bolger-baggins
What is scalar timing theory?
8 years ago