Academic journal article Memory & Cognition

The Numerical Distance Effect Is Task Dependent

Academic journal article Memory & Cognition

The Numerical Distance Effect Is Task Dependent

Article excerpt

Abstract Number comparison tasks produce a distance effect e.g., Moyer & Landauer (Nature 215: 1519-1520, 1967). It has been suggested that this effect supports the existence of semantic mental representations of numbers. In a matching task, a distance effect also appears, which suggests that the effect has an automatic semantic component. Recently, Cohen (Psychonomic Bulletin & Review 16: 332-336, 2009) suggested that in both automatic and intentional tasks, the distance effect might reflect not a semantic number representation, but a physical similarity between digits. The present article (1) compares the distance effect in the automatic matching task with that in the intentional number comparison task and suggests that, in the latter, the distance effect does include an additional semantic component; and (2) indicates that the distance effect in the standard automatic matching task is questionable and that its appearance in previous matching tasks was based on the specific analysis and design that were applied.

Keywords Number processing, automaticity . Automatic processing, attention

In 1967, Moyer and Landauer presented participants with two different digits between 1 and 9. Participants were asked to decide which digit, the right digit or the left, was numerically larger. It was found that response time (RT) increased as the distance between the digits decreased (e.g., RT was shorter for the pair "1 9" than for the pair "1 2"). This effect is known as the distance effect. The purpose of this article is to investigate whether the distance effect in this task is a result of the need to differentiate between overlapping semantic representations or whether it can only be attributed to the need to differentiate graphic similarity between digits (such as 8 and 9, both of which have circles on their tops). In addition, the aim of this article is to reinvestigate the automatic emergence of the distance effect in the matching task and, consequently, the theoretical notions that can be drawn from that task.

The source of the distance effect: semantic or physical

The distance effect can be explained by two components: physical and semantic. The semantic explanation takes into account the fact that digits are not just shapes but carry an important semantic content of quantity. The mental representation of a digit's semantic content is the source of the distance effect. Some theories suggest that numbers are semantically represented in analogical form. For example, the spatial mental number line theory suggests that a presented digit is converted to a mental representation along a spatial mental number line. When two digits are presented, they are converted into mental number representations on the same spatial mental line. This form of representation follows a very simple perception-like law: When two numbers on the same line are located close to each other (e.g., 1, 2), it is difficult to distinguish between them, since the encoding or the retrieval is impeded. As the number representations are located farther from each other, the distinction between them becomes easier. Because it is assumed that the efficiency of distinction is reflected in RT, Moyer and Landauer's (1967) distance effect can be explained by this theory (e.g., Dehaene & Changeux, 1993; Dehaene, Dupoux & Mehler 1990; Moyer, 1973). Other examples of the semantic representation of numbers that can explain the distance effect are the semantic network explanation (e.g., Whalen, 1996), the semantic coding theory (e.g., Banks, 1977), and memory-based theories that suggest that each number is attached to small or large attributes (e.g., Choplin & Logan, 2005; Leth-Steensen & Marley, 2000; Tzelgov, Meyer & Henik 1992).

In contrast to the theories that explain the distance effect by semantic representation, it has been suggested that the effect can also be explained by physical similarity. Recently, Cohen (2009) suggested that numerical symbols might initially have been created in such a way that their physical shape reflects the quantities they represent. …

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