Short Article: Coding Strategies in Number Space: Memory Requirements Influence Spatial–Numerical Associations

Abstract

The tendency to respond faster with the left hand to relatively small numbers and faster with the right hand to relatively large numbers (spatial numerical association of response codes, SNARC effect) has been interpreted as an automatic association of spatial and numerical information. We investigated in two experiments the impact of task-irrelevant memory representations on this effect. Participants memorized three Arabic digits describing a left-to-right ascending number sequence (e.g., 3–4–5), a descending sequence (e.g., 5–4–3), or a disordered sequence (e.g., 5–3–4) and indicated afterwards the parity status of a centrally presented digit (i.e., 1, 2, 8, or 9) with a left/right keypress response. As indicated by the reaction times, the SNARC effect in the parity task was mediated by the coding requirements of the memory tasks. That is, a SNARC effect was only present after memorizing ascending or disordered number sequences but disappeared after processing descending sequences. Interestingly, the effects of the second task were only present if all sequences within one experimental block had the same type of order. Taken together, our findings are inconsistent with the idea that spatial–numerical associations are the result of an automatic and obligatory cognitive process but do suggest that coding strategies might be responsible for the cognitive link between numbers and space.

When time is space: Evidence for a mental time line

“…Müller and Schwarz (2008) showed that, in number comparison on sequentially presented digits, ascending pairs (such as 2-3) yielded faster responses than descending pairs (3-2), suggesting that judgments about numbers reflect the temporal numerical order in which they are presented (see Ben-Meir et al, in press, for a further characterization of the effect). Previous studies have shown that, upon presentation of two tones with different durations, responses were more accurate when the first tone was shorter or the second tone was longer (Conson et al, 2008) as if a preference for increasing temporal intervals would exist (see Lindemann et al, 2008, for a similar finding in the numerical domain). Nicholls et al (2011) questioned the results of Schwarz and Eiselt (2009) and suggested that some associations between dimensions such as size, duration, and number can be in fact due to response biases rather than to the presence of common cognitive processes.…”

Addition goes where the big numbers are: evidence for a reversed operational momentum effect

“…Importantly, SNARC was not diluted as a result of the inverted spatial-numerical mappings trained in the arithmetic pointing tasks, so there was no correlation between the spatial biases obtained for mental arithmetic and for single digits following the arithmetic task. Thus, despite establishing the context sensitivity of OM, we were unable to demonstrate with the present design a similar sensitivity for task specificity of SNARC, which had been shown in previous studies (e.g., Bächtold et al, 1998;Dehaene et al, 1993;Fischer et al, 2010;Lindemann et al, 2008;Notebaert et al, 2006;Ristic et al, 2006;van Dijck et al, 2014). Therefore, we cannot confirm the hypothesis that OM and SNARC rely on a shared mechanism.…”

“…For example, SNARC disappears when simultaneously remembering a number sequence in descending order (Lindemann, Abolafia, Pratt, & Bekkering, 2008;see also van Dijck, Abrahamse, Acar, Ketels, & Fias, 2014) or when numbers appear in spatially incongruent positions (e.g., Fischer, Mills, & Shaki, 2010). SNARC for a given number can even be reversed by manipulating the task instructions (Bächtold, Baumüller, & Brugger, 1998; see also Ristic, Wright, & Kingstone, 2006), by presenting it within either smaller or larger numbers (Dehaene et al, 1993, Exp. 3), or by interleaving SNARC assessment with spatially incongruent responses in another task (Notebaert, Gevers, Verguts, & Fias, 2006; see also Bae, Choi, Cho, & Proctor, 2009;Pfister, Schroeder, & Kunde, 2013).…”

Visuospatial bootstrapping: Evidence for binding of verbal and spatial information in working memory

“…If spatial bootstrapping processes based on the number line had been in operation, then performance should have been best in the linear display condition. Lindemann, Abolafia, Pratt and Bekkering (2008) recently showed that SNARC-type number line effects were not a consequence of obligatory encoding of numbers in a number line format, arguing instead that SNARC effects were likely to arise from top-down strategic processes. Our data are certainly consistent with the idea that number line effects are not obligatory, and if strategic processes were adopted in this task, using a linear number line was not the strategy that was selected.…”