Visual Number Beats Abstract Numerical Magnitude: Format-dependent Representation of Arabic Digits and Dot Patterns in Human Parietal Cortex

Abstract

In numerical cognition, there is a well-known but contested hypothesis that proposes an abstract representation of numerical magnitude in human intraparietal sulcus (IPS). On the other hand, researchers of object cognition have suggested another hypothesis for brain activity in IPS during the processing of number, namely that this activity simply correlates with the number of visual objects or units that are perceived. We contrasted these two accounts by analyzing multivoxel activity patterns elicited by dot patterns and Arabic digits of different magnitudes while participants were explicitly processing the represented numerical magnitude. The activity pattern elicited by the digit "8" was more similar to the activity pattern elicited by one dot (with which the digit shares the number of visual units but not the magnitude) compared to the activity pattern elicited by eight dots, with which the digit shares the represented abstract numerical magnitude. A multivoxel pattern classifier trained to differentiate one dot from eight dots classified all Arabic digits in the one-dot pattern category, irrespective of the numerical magnitude symbolized by the digit. These results were consistently obtained for different digits in IPS, its subregions, and many other brain regions. As predicted from object cognition theories, the number of presented visual units forms the link between the parietal activation elicited by symbolic and nonsymbolic numbers. The current study is difficult to reconcile with the hypothesis that parietal activation elicited by numbers would reflect a format-independent representation of number.

The integration between nonsymbolic and symbolic numbers: Evidence from an EEG study

“…A classifier trained to differentiate quantities within one format (e.g., Arabic numeral) could not differentiate as well between quantities presented in another format (e.g., nonsymbolic numbers). Similar results of classification accuracies as well as generalization were found in other fMRI studies (Bulthé, De Smedt, & de Beeck, 2014, 2015; Lyons, Ansari, & Beilock, 2015), suggesting that even though IPS is responsive to numerical information in general, nonsymbolic and symbolic numbers are not represented in the same way in IPS.…”

The Dorsal Attention Network Reflects Both Encoding Load and Top–down Control during Working Memory

“…physical numerosity is held constant. Intraparietal cortex is known to react to differences in numerosity, particularly for physical differences (e.g., different visual quantities) as opposed to abstract differences (e.g., digits symbolizing different numerical quantities; Bulthe et al, 2015;Piazza et al, 2004Piazza et al, , 2007. In this study, the sensory events were matched in high and low load conditions as the number of temporally/visually separated physical stimuli was the same in both conditions.…”

“…We know from studies in the numerical domain that the intraparietal sulci are sensitive to numerosity information for physical objects and their univariate activation levels change when the amount of physical stimuli presented on the screen changes, and this even in passive viewing tasks (Piazza, Pinel, Le Bihan, & Dehaene, 2007;Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004). Bulthe, De Smedt, and Op de Beeck (2015) further showed that multivariate signals in the parietal cortex are particularly sensitive to physical differences in numerosity (one dot vs. five dots), rather than abstract differences of numerosity (the number "1" vs. the number "5"). It follows that the univariate activity differences observed in the intraparietal sulcus for WM sets differing in stimulus load may also reflect the differences in physical numerosity and not only differences in WM load per se.…”

The Source of the Symbolic Numerical Distance and Size Effects

“…Additionally and more importantly, an increasing number of findings are not in line with the ANS model. For example, symbolic and non-symbolic performance seems to be independent on many behavioral (Holloway and Ansari, 2009; Sasanguie et al, 2014; Schneider et al, 2016) and neural level (Damarla and Just, 2013; Bulthé et al, 2014, 2015; Lyons et al, 2015). In a correlational study it has been shown that distance and size effects dissociate in Indo-Arabic comparison task (Krajcsi, 2016).…”

“…For example, it has been shown that performance of the symbolic and non-symbolic number comparison tasks do not correlate in children (Holloway and Ansari, 2009; Sasanguie et al, 2014), and in an fMRI study the size of the symbolic and non-symbolic number activations did not correlate (Lyons et al, 2015). As another example, whereas former studies found common brain areas activated by both symbolic and non-symbolic stimuli (Eger et al, 2003; Piazza et al, 2004), later works with more sensitive methods found only notation-dependent activations (Damarla and Just, 2013; Bulthé et al, 2014, 2015). According to an extensive meta-analysis, although it was repeatedly found that simple number comparison task (the supposed sensitivity of the ANS) correlates with mathematical achievement, it seems that non-symbolic comparison correlates much less with math achievement, than symbolic comparison (Schneider et al, 2016).…”