Abstract:
Numbers are fundamental to everyday life, and understanding their cognitive processing and mental representations is therefore essential. A key phenomenon in the field of numerical cognition is the Spatial-Numerical Association of Response Codes (SNARC) effect, which refers to faster responses to small numbers with the left hand and to large numbers with the right hand (Dehaene et al., 1993). This dissertation addresses several controversies surrounding the SNARC and SNARC-like effects in six large (mostly online) studies. Typically, the SNARC effect is investigated in bimanual decision tasks using number stimuli from 1 to 9 (excluding 5). Task-relevant features include number magnitude or ordinality (e.g., magnitude classification: smaller vs. larger than 5), other semantic features (e.g., parity judgment: odd vs. even), or non-semantic features (e.g., color judgment: blue vs. yellow). We found that the SNARC effect follows a continuous pattern in parity judgment (i.e., gradually increasing right relative to left association with increasing number magnitude), but a more categorical pattern in magnitude classification (i.e., similar left association for small and right association for large numbers; Studies 2 and 3). Despite mixed prior findings, we also observed a SNARC effect in color judgment, albeit weaker and driven only by small numbers (Study 1). Thus, while the processing and mental representations of numbers are highly automatic, their shape and strength depend on task demands. Both also seem to depend on language script direction and other cultural directional preferences. However, even with right-to-left language script, we did not observe a full reversal of the group-level SNARC effect (Study 3). Beyond numbers, SNARC-like effects extend to other ordinal stimuli. For letters, we found spatial mappings consistent with alphabetical order and, when made sufficiently salient, also with the order in newly memorized sequences (Study 4). Relatedly, while we replicated that the SNARC effect depends on relative magnitude or ordinality within the number set, it also seems to depend on absolute magnitude or ordinality (Study 5). Hence, the SNARC and SNARC-like effects are partly flexible, relying on working memory, and partly fixed, relying on long-term memory. Finally, we investigated the inter- and intraindividual variability of the SNARC effect. Only about half the sample showed a reliable SNARC effect in color judgment (Study 1), similar to prevalence rates reported for magnitude classification and parity judgment. Our novel longitudinal design (the “Ironman paradigm”) revealed that the temporal stability of the SNARC effect in parity judgment was low and unsystematic (Study 6). Taken together, these studies simultaneously highlight the robustness and the variability of spatial mental representations of magnitude and ordinality. The SNARC and SNARC-like effects are shaped by task instructions, cultural background, and memory content, and are further characterized by inter- and intraindividual differences. Based on the findings of all studies, a computational contextualization model is introduced, building upon the assumption that the combination of simultaneously activated cognitive context schemata drives the SNARC and SNARC-like effects. Preliminary results obtained from initial data simulations and parameter optimization are promising, suggesting that the model may account for different shapes and strengths of the effects, as well as for their high variability.
SNARC effect