Physical Similarity or Numerical Representation Counts in Same–Different, Numerical Comparison, Physical Comparison, and Priming Tasks?

Abstract

Recent studies have highlighted the fact that some tasks used to study symbolic number representations are confounded by judgments about physical similarity. Here, we investigated whether the contribution of physical similarity and numerical representation differed in the often-used symbolic same-different, numerical comparison, physical comparison, and priming tasks. Experiment 1 showed that subjective physical similarity was the best predictor of participants' performance in the same-different task, regardless of simultaneous or sequential presentation. Furthermore, the contribution of subjective physical similarity was larger in a simultaneous presentation than in a sequential presentation. Experiment 2 showed that only numerical representation was involved in numerical comparison. Experiment 3 showed that both subjective physical similarity and numerical representation contributed to participants' physical comparison performance. Finally, only numerical representation contributed to participants' performance in a priming task as revealed by Experiment 4. Taken together, the contribution of physical similarity and numerical representation depends on task demands. Performance primarily seems to rely on numerical properties in tasks that require explicit quantitative comparison judgments (physical or numerical), while physical stimulus properties exert an effect in the same-different task.

Limited-capacity identity processing of multiple integers

“…Although Model 1g can accommodate the present data, we may ask why effects of numerical distance arose here, when similar effects have not been present in other digit identity tasks when physical similarity was taken into account Cohen (2009;see also García-Orza et al, 2012, andZhang et al, 2018). This appears surprising, given that digit identification was the basic task in Cohen's (2009) earlier study, as it was here.…”

“…Similarly, if one is presented with the sounds "fīv," it is possible to access the corresponding quantity demanded by a mental arithmetic problem. However, cases are beginning to emerge in which task performance does not depend on such cross-talk (Cohen, 2009;García-Orza et al, 2012;Zhang et al, 2018), as well as cases in which the operation of a processor is revealed even though successful task completion does not demand it (as in the experiments here). Such demonstrations should be considered against other cases in which effects are clearly context-dependent and emerge only as a consequence of the task constraints (see, e.g., Campbell, 2011;Cohen & Dehaene, 1995).…”

“…As such, this work is akin to that undertaken by researchers in their quest to understand how processes concerning visual featural and letter encoding inform more general theories concerning the mental architecture underpinning word recognition and reading (see, e.g., McClelland & Rumelhart, 1981;Rumelhart & Siple, 1974). Although, historically, these "low-level" processes have not featured heavily in traditional accounts, there is now a growing body of evidence that these need to be considered if adequate models of numerical cognition are to be developed (see Cohen, 2009Cohen, , 2010Cohen & Quinlan, 2016;Cohen, Warren, & Blanc-Goldhammer, 2013;Defever, Sasangie, Vandewaetere, & Reynvoet, 2012;García-Orza, Perea, Mallouh, & Carreiras, 2012;Wong & Szücs, 2013;Zhang, Xin, Feng, Chen, & Szücs, 2018).…”

“…Not considered here, in any detail, are models in which digit identity can be completed solely through the quantity processor. These models would predict an effect of numerical distance but not physical similarity, and given the emerging evidence against this pattern, this outcome is taken to be extremely unlikely and not considered further (Cohen, 2009;Cohen et al, 2013;Defever et al, 2012;García-Orza et al, 2012;Wong & Szücs, 2013;Zhang et al, 2018).…”

Further insights into the operation of the Chinese number system: Competing effects of Arabic and Mandarin number formats

“…Such a pattern of results clearly emphasizes the fact that the physical characteristics of the numerical stimuli cannot be ignored in accounting for performance across a range of numerical tasks. Indeed, such a conclusion has now extensive support in the literature (see Cohen, 2009Cohen, , 2010Cohen & Quinlan, 2016;Defever, Sasanguie, Vandewaetere, & Reynvoet, 2012;Garciá-Orza, Perea, Mallouh, & Carreiras, 2012;Lin & Göbel, 2019;Wong & Szücs, 2013;Zhang, Xin, Feng, Chen, & Szücs, 2018).…”