Academic journal article Attention, Perception and Psychophysics

Is 26 + 26 Smaller Than 24 + 28? Estimating the Approximate Magnitude of Repeated versus Different Numbers

Academic journal article Attention, Perception and Psychophysics

Is 26 + 26 Smaller Than 24 + 28? Estimating the Approximate Magnitude of Repeated versus Different Numbers

Article excerpt

Published online: 28 October 2011

© Psychonomic Society, Inc. 2011

Abstract It has recently been suggested that regardless of the dimension at hand (i.e., numerosity, length, time), similar operational mechanisms are involved in the comparison process based on approximate magnitude representation. One piece of evidence for this hypothesis lies in the presence of similar behavioral effects for any comparison (i.e., the distance effect). In the case of length comparison, the comparison process can be biased by summation toward either an underestimation or an overestimation: The sum of equal-size stimuli is underestimated, whereas the sum of different-size stimuli is overestimated. Relying on the hypothesis that similar operational mechanisms underlie the comparison process of any magnitude, we aim at extending these findings to another magnitude dimension. A number comparison task with digit numbers was used in the two experiments reported presently. The objective was to investigate whether summation also biases magnitude representation of numerical and symbolic information. The results provided evidence that the summation bias can also apply to numerical magnitude comparison, since the sum of repeated numbers (26 + 26) was underestimated whereas the sum of different numbers (24 + 28) was overestimated. We propose that these effects could be accounted for by a heuristic linking cognitive effort and magnitude estimation.

Keywords Approximate magnitude . Comparison process . Numerical cognition

In a numerical comparison task in which participants have to judge, for example, whether a numerosity is inferior or superior to 5, reaction times (RTs) are longer and accuracy is lower when responding to numerosity "4" than to "1" (see Fig. 1a). This effect, known as the distance effect, refers to the fact that the longer the time required to judge whether two magnitudes differ the shorter the distance between the two magnitudes (Dehaene, 1996; Moyer & Landauer, 1967). Interestingly, numerical judgments based on symbolic information (i.e., digits) show a similar distance effect, revealing that numerical comparisons based on symbolic and nonsymbolic information might involve similar mechanisms and rely on analogous magnitude representation (Butterworth, 1999; Dehaene, 1997; Piazza, Pinel, Le Bihan, & Dehaene, 2007; Shuman & Kanwisher, 2004). At a neuronal level, numerical comparisons with symbolic and nonsymbolic information entail the activation of the horizontal segment of the intraparietal sulcus (Piazza et al., 2007). On the basis of this behavioral and neuroimaging evidence, a common magnitude system for number and numerosity has been proposed (Dehaene, 1996; Gallistel & Gelman, 1992, 2000; Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004). This system is supposed to underlie the transformation of discrete events into analogous representation of numerical magnitude (for a review, see Brannon, 2006; see also Pinel, Dehaene, Riviere, & Le Bihan, 2001; Pinel, Piazza, Le Bihan, & Dehaene, 2004). Symbolic numerical information would be automatically transformed into analogous magnitude representation (Dehaene, Dehaene-Lambertz, & Cohen, 1998). Some authors have suggested that this magnitude system could be involved in dimensions other than number, such as space and time, for instance (see Hubbard, Piazza, Pinel, & Dehaene, 2005; Kaufmann et al., 2005; Walsh, 2003). Although it still remains controversial to declare the existence of a shared magnitude representation system (Bueti&Walsh, 2009; Cappelletti, Freeman, & Cipolotti, 2009; Cohen Kadosh et al., 2005; Pinel et al., 2004), it seems commonly admitted that the mechanisms used for numerical magnitude comparison are similar to those used for physical comparison (Cantlon, Platt, & Brannon, 2009; Gallistel & Gelman, 1992, 2000). One piece of evidence accounting for this claim comes from the presence of the distance effect in any comparison task, regardless of the dimension (i. …

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