Why spatial-numeric associations aren't evidence for a mental number line

Why Spatial-Numeric Associations Aren’t Evidence for a Mental Number Line David H. Landy (dlandy@uiuc.edu) Department of Psychology, 603 E. Daniel Street University of Illinois at Urbana Champaign Champaign, Illinois USA Erin L. Jones (eljones3@uiuc.edu) Department of Psychology, 603 E. Daniel Street University of Illinois at Urbana Champaign Champaign, Illinois USA John E. Hummel (jehummel@uiuc.edu) Department of Psychology, 603 E. Daniel Street University of Illinois at Urbana Champaign Champaign, Illinois USA numerical magnitude (as in Dehaene et al. (1993) and in the current paper, where the task was to determine whether the number was even or odd), people respond more rapidly to large numbers with their right hand, and more rapidly to small numbers with their left hand. The direction of this effect (termed the Spatial-Numeric Association of Response Codes, or SNARC effect) seems to correspond to typical writing direction (Zebian, 2005), suggesting that the association is acquired (but see Hubbard et al., 2004). The usual explanation of the SNARC effect takes the system of linearizing numbers utilized in keyboards and in number lines and cognitively reifies it, by assuming that numbers are represented spatially, i.e., along a mental number line. Thus, the mental representation of ‘9’ includes the property “right of 2”. Note that the posited code is relative—9 is represented as being more right than, say, 2, but leftward of 20. The SNARC effect, then, results from the fact that the representation of a large number overlaps more with the representation of a right-hand response than it does with that of a left-hand response. This account—which we will call a ‘representational overlap account—has been used to explain a wide variety of effects relating to sides of space and numerical magnitude (e.g., Fischer, 2001; Casarotti et al., 2007). A very similar representational overlap account has been used to explain the well-known Simon effect (Simon, 1990). In a typical experiment illustrating the Simon effect, participants respond to non-spatial properties of simple stimuli, such as color, using a right-hand and a left-hand response. Responses are facilitated when the side of correct response corresponds to the side of presentation, even though side of presentation is formally irrelevant to the task. As in the mental number-line account of the SNARC effect, the stimulus-response compatibility arises from the overlapping spatiality in representation of stimulus and response. Recently, a different kind of account has been proposed that explains the SNARC effects along with the Simon effect under a framework that does not involve representational spatial overlap. With this account, called Abstract In the well-known SNARC effect, people are shown to be faster at responding to relatively large numbers with their right hands, and to relatively small numbers with their left hands, on magnitude-irrelevant tasks. It is typically assumed that both the SNARC effect and the Simon effect—in which right-hand responses are facilitated when stimuli appear on the right-hand side—are explained by spatial mappings of stimulus to response; where the former is the result of representing numbers spatially (i.e. along a mental number line) and mapping right-hand responses to large numbers and left-hand responses to small numbers, and the latter is the result of responding to stimuli on the right side of visual space with the right hand and vice-versa. However, the principle of polarity correspondence can also account for these findings; this theory asserts that in binary representations of dimensions, one pole is dominant and tasks are facilitated when dominant stimulus values are mapped to dominant response values. In previous studies, dominance and spatial mapping have been confounded. The current paper uses non-spatial responses (spoken “yes” and “no” responses) to consider whether polarity correspondence can account for the SNARC effect. Keywords: Mathematical Cognition; SNARC Stimulus-Response Compatibility; Simon Effect. effect; Introduction The number keys on a typical American or European keyboard are laid out with small numbers on the left, and larger numbers on the right. On a telephone keypad, the numbers are arranged with small on the left, and large on the right. In school students are taught to reason using a “number line”, which arrays the numbers in linear order, with (guess what? ) small numbers on the left, and large numbers on the right. Dehaene, Bossini, and Giraux (1993) demonstrated that people respond to small numbers in a spatially asymmetric way. Even when the task requires minimal processing of