In a clearly written and thought provoking article, Cohen Kadosh & Walsh (CK&W) make three interrelated arguments. First, they claim that the meaning of numerals – numerical magnitude – is activated in an automatic fashion just about whenever a numeral is presented for view. Second, they argue that notation-induced differences in processing can be tapped when one does not impose an intentional task, indeed any task, engaging the presented numerals. Third, they suggest that the best behavioral avenue to uncover the effect of notation is to perform Stroop-like conflict studies in which the different notations serve in turn as the target and the to-be-ignored dimensions. The generic view advanced by the authors has merit, but there are difficulties with the arguments.

Concerning the first argument, the authors pinpoint the vast experience that humans have with numbers and conclude that, as a result, numbers are over-learned and processed in an automatic fashion. Numbers are certainly ubiquitous in people's cognitive milieu, but it does not follow that the full arithmetic properties of a number are activated in an obligatory fashion just whenever a number is presented for any purpose. As Stevens noted in his celebrated chapter, a numeral can be “an ink mark on a piece of paper” (Stevens Reference Stevens and Stevens1951, p. 22); another intellectual giant of quantitative psychology has similarly remarked that numerals can sometimes be mere “scratches on paper” (Guilford Reference Guilford1954, p. 5). Human cognition is a wonderfully adjustable system, flexible enough to treat numerals as mere shapes when that suffices to perform the task (if there is one to perform). This conclusion was reached in a tightly controlled study by Cohen (Reference Cohen2009). Cohen presented participants with a single numeral (between 1 and 9) and asked perhaps the simplest possible question: to identify whether the presented numeral was a 5. If numbers automatically activate their magnitude representations, then reaction time should be a function of the distance between 5 and the presented numeral. Instead, magnitude information did not affect the data, only physical shape did. Cohen (Reference Cohen2009) concluded that “numerical symbols do not automatically activate quantity representations” (p. 336) and that, in the absence of meaning, the shapes determine the results. Ratinckx et al. (Reference Ratinckx, Brysbaert and Fias2005) reached similar conclusions with respect to two-digit numerals.

Typical markers of automatic activation mentioned by the authors, such as the size congruity effect, are also inconsistent with a sharp dichotomy between automatic and intentional processing. Virtually all studies that demonstrated the effect (of task-irrelevant numerical magnitude on judgments of physical size) used a design that favored the numerical over the physical dimension in the first place. Thus, more values of number than values of physical size were typically presented (indeed, most studies used merely two values for size: large, small). Moreover, the numerals were easier to discriminate from one another than their physical sizes. When these and further contextual biases were removed (Algom et al. Reference Algom, Dekel and Pansky1996; Pansky & Algom Reference Pansky and Algom1999; Reference Pansky and Algom2002), the size congruity effect evaporated – with the numbers processed as mere shapes. And, when physical size is made the more salient dimension (Fitousi & Algom Reference Fitousi and Algom2006) the size congruity effect reverses with physical size intruding on number magnitude more than vice versa. Such pliability is inharmonious with (strongly) automatic processing. The absence of automatic activation of (cardinal) numerical magnitude has been shown with respect to another marker of automatic activation, the SNARC effect (Ben-Nathan et al. Reference Ben-Nathan, Shaki, Salti and Algom2009). Of even more concern, these two putative markers of automatic activation were unrelated for the same numbers with the same observers (Fitousi et al. Reference Fitousi, Shaki and Algom2009).

The upshot is that (a) automatic and intentional processing do not form a dichotomy, but rather, mark the end-points of a finely grained continuum, and that (b) the dominant type processing is under strong contextual control. Consequently, numerical magnitude is not activated in an automatic fashion on an unlimited scale; it is not the default processing option when a numeral is presented for view. When contextual demands do not invite number processing, the presented numerals may well be processed as mere shapes or marks. Therefore, it is not prima facie clear what the recordings in the adaptation paradigms with passive viewing signify. They might not be pure measures of number processing (note: numerals in different notation differ in shape). Alternatively, some features (demand characteristics?) of the experimental situation might have invited/encouraged number processing. Be that as it may, passive viewing seems to be a suboptimal vehicle to test notation-induced differences in processing. CK&W seem to admit this when they mention that the experimenter cannot know what aspect of the stimulus the observers elect to attend.

Given the fuzzy demarcation of automatic processing, I do not fully agree with the second claim made by the authors that the effect of notation should be tested via automatic processing. Of course, the authors can retort that, regardless of the generic question of automaticity, the testing can take place in those conditions in which automatic processing has been verified in advance (e.g., a size congruity effect is demonstrated for the stimuli). Note that this stipulation cannot apply with passive viewing. However, I am not convinced that intentional processing is inherently unsuitable for testing the effects of notation. Surely, strategies can bias processing but they do not invariably act to produce a common abstract representation. Thus, Fias (Reference Fias2001) did find a dissociation between a parity judgment task and a phoneme verification task with verbal numbers, even though magnitude information is not needed for performance in both tasks. Damian (Reference Damian2004) demonstrated a task-dependent asymmetry in performance across Arabic and verbal numerals. So, I would not rule out intentional processing as platform for testing the question of notational effects.

Concerning the third argument, by a fortuitous coincidence, Ben-Nathan (Reference Ben-Nathan2009; Ben-Nathan & Algom Reference Ben-Nathan, Algom, Schneider, Ben-David, Parker and Wong2008) performed the experiment recommended by the authors: A pair of numerals appeared on each trial, an Arabic digit and a verbal number, and the participants decided, while timed, whether the number in the target notation was larger or smaller than a standard number. The Stroop effect for each notation was calculated as the difference in performance between congruent and incongruent displays. As the results show (Fig. 1), both Arabic and word performance was affected by the irrelevant number in the alternative notation, although the effect was greater for word. This set of data is not completely decisive, but the Stroop effects recorded for both notations tap a considerable amount of common, hence abstract, processing.

Figure 1.

The time needed to decide the numerical magnitude (larger or smaller than the standard) as a function of target notation and congruity. [Con: congruent, Incon: incongruent].