As indicated by Cohen Kadosh & Walsh (CK&W), looking at automatic processing provides an informative insight into the nature of the underlying numerical representations that are relatively uncontaminated by task-dependent strategies. Automatic numerical processing was explored in past research using two main paradigms. The first was the size congruency paradigm, showing that automatic numerical processing takes place when participants intentionally compare the physical sizes of numerical stimuli. Of particular relevance are recent works by Cohen Kadosh et al. (Reference Cohen Kadosh, Henik and Rubinsten2008e) and Ganor-Stern and Tzelgov (Reference Ganor-Stern and Tzelgov2008), which examined automatic processing of numerical magnitude for digits and number words, and for numbers in Arabic and Indian notations. The second paradigm was the SNARC effect, showing automatic magnitude processing and mapping of magnitude to space when participants perform a variety of tasks that do not require magnitude processing. Relevant for the present context are works that looked at the SNARC effect for digits and number words (e.g., Fias et al. Reference Fias, Brysbaert, Geypens and d'Ydewalle1996; Nuerk et al. Reference Nuerk, Wood and Willmes2005).

The target article authors' conclusion from past studies is that the representation underlying automatic processing is notation-specific. This conclusion is mainly based on the fact that the evidence for automatic numerical processing was not identical for the different notations. In this commentary, I suggest that a notation-specific representation does not necessarily follow from the empirical findings, and I propose alternative explanations for the patterns of findings reviewed in detail in the target article.

First, CK&W have cited a series of studies showing more robust evidence for automatic processing of digits than of number words, and have interpreted this pattern of results as supporting the idea of notation-specific representation. It should be noted, however, that automatic processing is heavily influenced by skill level. People are not equally skilled with extracting numerical information from different notations, but rather, they are more skilled in extracting such information from digits than from number words. As a consequence, automatic numerical processing of number words might be more limited than that of digits. Hence, it might take longer time to occur (Cohen Kadosh et al. Reference Cohen Kadosh, Henik and Rubinsten2008e), it might not take place when a verbal task is performed (Fias et al. Reference Fias, Lauwereyns and Lammertyn2001a), or under some conditions, it might not occur at all (Ito & Hatta Reference Ito and Hatta2003). Thus, it is possible that there is a common underlying abstract representation, but it could be that it takes longer to access it from a number word compared to a digit. In some cases the processing of the relevant dimension is fast enough so that the relatively slow process of accessing the abstract numerical representation from the number word does not interfere with it.

Second, CK&W have based their argument for a notation-specific representation underlying automatic processing on the fact that the size congruency effect took a slightly different form for the different notations (Cohen Kadosh et al. Reference Cohen Kadosh, Henik and Rubinsten2008e; Ganor-Stern & Tzelgov Reference Ganor-Stern and Tzelgov2008). The problem with the argument is that this effect reflects the interaction between the processing of the relevant and irrelevant dimensions, and a difference in this interference effect between notations might stem from the relevant physical size dimension and not from the irrelevant numerical one. Therefore, this should not be seen as evidence for a notation-specific underlying representation. For example, in Dehaene and Akhavein's (Reference Dehaene and Akhavein1995) study, the absence of a distance effect in the physical same-difference task for pairs composed of a digit and a number word may very well be due to the fact that such pairs are so physically dissimilar – which makes the decision faster and, as a consequence, too short to be affected by the processing of the irrelevant dimension. Indeed, our recent study that used two numerical notations (Arabic and Indian) was able to show evidence for automatic numerical processing when the numbers were presented in different numerical notations (Ganor-Stern & Tzelgov Reference Ganor-Stern and Tzelgov2008).

The debate over the interpretation of Ganor-Stern and Tzelgov (Reference Ganor-Stern and Tzelgov2008) or Cohen Kadosh et al. (Reference Cohen Kadosh, Henik and Rubinsten2008e) seems to be a case of which half of the glass you are looking at. In my opinion, the fact that incongruency between numerical and physical sizes affected performance in the physical task, even in mixed-notation pairs, seems to be especially strong evidence for the idea of an abstract representation (Ganor-Stern & Tzelgov Reference Ganor-Stern and Tzelgov2008). More support is provided by studies reporting a size congruency effect not only for numbers but also for number words (Ansari et al. Reference Ansari, Fugelsang, Dhital and Venkatraman2006b; Cohen Kadosh et al. Reference Cohen Kadosh, Henik and Rubinsten2008e). CK&W, in contrast, seem to focus on the empty half of the glass and to spotlight the differences in the pattern of results for the different notations. As explained earlier, some of these differences might be a product of other factors and are not informative as to the nature of the underlying numerical representation; and some may even be accidental.

More generally, it seems that the authors set the criterion that any non-additive difference between the numerical processing of the different notations is evidence for a notation-specific representation. This criterion might be too lenient, as not all differences are theoretically relevant for the issue in question. As explained earlier, some of the differences are due to skill level, some are due to the nature of the relevant dimension, and some are truly accidental. In the debate over the issue of abstract/non-abstract representation, attention should be given only to such differences that are either theoretically interpretable or at least that are replicable across studies.

Finally, one of the main points made by the target article is the importance of studying automatic processing in addition to intentional processing. Behavioral studies indeed provided evidence for dissociable patterns of results in the two modes of processing (Ganor-Stern et al. Reference Ganor-Stern, Tzelgov and Ellenbogen2007; Tzelgov et al. Reference Tzelgov, Ganor-Stern and Maymon-Schreiber2009). Unfortunately, brain-imaging studies that looked at intentional and automatic numerical processes did not report such a dissociation in terms of different electrophysiological activity, or areas being active when the two modes of processing were taking place (Ansari et al. Reference Ansari, Fugelsang, Dhital and Venkatraman2006b; Cohen Kadosh et al. Reference Cohen Kadosh, Cohen Kadosh, Linden, Gevers, Berger and Henik2007c). Future neuropsychological research should attempt to dissociate these two types of processes in terms of the underlying brain activation.