A novel regression approach and behavioral primacy of number

Non-numerical features of an item array are necessarily partially correlated with number. Nevertheless, as demonstrated in DeWind et al. (Reference DeWind, Adams, Platt and Brannon2015), an appropriately designed stimulus set can vary each feature such that they are partially independent from number and from each other and can be reduced to a common basis set (number, size, and spacing). As with any regression analysis, our approach leverages the unique variance of each feature to determine which feature affects the variance in a dependent measure, whether it is behavior (DeWind et al. Reference DeWind, Adams, Platt and Brannon2015) or neural activity (Park et al. Reference Park, DeWind, Woldorff and Brannon2016b). In particular, that regression approach provides a way to test the degree to which participants use non-numerical response strategies in a numerical comparison task. Critically, participants made comparisons on the basis of number, and much more so on number than other visual features (DeWind et al. Reference DeWind, Adams, Platt and Brannon2015).

Passive viewing paradigm

Numerosity judgments are influenced by non-numerical cues and vice versa, and such influences are non-linear and asymmetric (Allik & Tuulmets Reference Allik and Tuulmets1993; Gebuis & Reynvoet Reference Gebuis and Reynvoet2012b; Ginsburg & Nicholls Reference Ginsburg and Nicholls1988; Miller & Baker Reference Miller and Baker1968; Mix et al. Reference Mix, Huttenlocher and Levine2002a; Nys & Content Reference Nys and Content2012; Soltesz et al. Reference Soltesz, Szucs and Szucs2010; Sophian & Chu Reference Sophian and Chu2008; Tokita & Ishiguchi Reference Tokita and Ishiguchi2013). Thus, the representation of one dimension (say, numerosity) will differ depending on whether the task requires focusing on numerosity or some other dimension. One can circumvent this issue by using a neural approach with a passive viewing paradigm. Indeed, using EEG to measure neural activity while participants were passively viewing dot arrays, we tested which magnitude dimension most contributes to the modulation of neural activity in a task-free design (Park et al. Reference Park, DeWind, Woldorff and Brannon2016b). However, the target article incorrectly states “a strong correlation between number and continuous magnitudes can change strategy [in our study]” (sect. 6, para. 2), when in fact there was no strategy involved.

Even under a passive viewing paradigm, attention might be directed toward one feature dimension over another because a larger range in one stimulus dimension may increase salience and consequently override the effects of another dimension with a smaller range. For an extreme example, imagine the apparent contrast of a set of 10 dots each with a radius of 1 cm and a set of 11 dots each with a radius of 0.1 cm. Clearly, the salience of the area difference would overwhelm the number difference, and neural activity modulated by such large salient differences in area could easily mask neural activity modulated by relatively less salient number differences. Therefore, it is important to use the same range of values in each magnitude dimension for a fair comparison between them. The target article incorrectly states that Park et al. (Reference Park, DeWind, Woldorff and Brannon2016b) used a greater range of continuous magnitudes, when across two experiments we indeed used dot arrays that were constructed to cover equal ranges of number, size, spacing, total area, item area, total perimeter, item perimeter, convex hull, density, coverage, and overall scale. In fact, in Park et al. (Reference Park, DeWind, Woldorff and Brannon2016b), we made this exact critique of the experimental design used by Gebuis and Reynvoet (Reference Gebuis and Reynvoet2013), which employed a larger range of continuous magnitudes than numerosity. The Leibovich et al. (Reference Leibovich, Vogel, Henik and Ansari2016b) article that the authors rely on to develop their thesis suffers from this criticism because there was a greater difference in non-numerical magnitudes (ratio of about 2:5) than in numerical magnitudes (ratio of about 3:5). Therefore, the observed smaller interference of numerosity in non-numerical magnitude compared with the reverse in that study could have been driven by differences in the ratios between the two dimensions. Collectively, the target article mischaracterizes the stimulus design in Park et al. (Reference Park, DeWind, Woldorff and Brannon2016b) and fails to recognize the implications of having unequal magnitude ranges in the very studies that it relies on to build the main thesis (e.g., Gebuis & Reynvoet Reference Gebuis and Reynvoet2013; Leibovich et al. Reference Leibovich, Vogel, Henik and Ansari2016b).

High-temporal-resolution recording of neural activity

The target article asks which magnitude dimension is more “basic, innate, and automatic” (sect. 5.1, para. 3). In fact, the main contribution of our event-related potential approach (in combination with the aforementioned stimulus design and regression approach) was the demonstration of selective neural sensitivity to numerosity very early in the visual stream, prior to any neural sensitivity to other non-numerical magnitudes (Park et al. Reference Park, DeWind, Woldorff and Brannon2016b). Such a robust and selective effect of numerosity with negligible effects of non-numerical magnitudes was demonstrated in two independent experiments in Park et al. (Reference Park, DeWind, Woldorff and Brannon2016b) and is now replicated in similar experiments investigating different neural index and different ranges of numerosities (Fornaciai & Park Reference Fornaciai and Park2017; Park Reference Park2017). These results directly contradict the authors' conclusion that the representation of numerical magnitude stems from continuous magnitudes. Instead, our findings support the idea that numerosity is perceived directly and rapidly in the visual stream.