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Evidence for Multiple Representations of Number in the Human Brain

Electrophysiological Evidence for Multiple Representations of Number in the Human Brain Frank Kanayet (kanayet.1@osu.edu) Department of Psychology, 255 Psychology Building Columbus, OH 43206 USA John Opfer (opfer.7@osu.edu) Department of Psychology, 245 Psychology Building Columbus, OH 43206 USA William Cunningham (cunningham.417@osu.edu) Department of Psychology, 100G Lazenby Hall Columbus, OH 43206 USA Abstract In adult human brains, the horizontal segment of the intraparietal sulcus plays a large role in representing numeric magnitude. In children and non-human primates, however, frontal cortex may play a larger role. We hypothesized that there is a link between observed developmental changes in locus of representation (frontal to parietal) and type of representation used (logarithmic to linear). Participants were presented with number lines and asked to judge accuracy of linear, logarithmic, or log-linear placements. Consistent with hypotheses, event-related potentials generally revealed greatest parietal N1 amplitudes for linear placements and greatest frontal P3 amplitude for logarithmic placements. Additionally, effects of linear placements on cortical activity were moderated by numerical magnitude: parietal N1 amplitudes decreased with magnitude, whereas frontal P3 amplitudes increased with magnitude. These results suggest adults possess logarithmic and linear representations of number, and when logarithmic representations were elicited; there was greater involvement of frontal cortex. Keywords: Numerical cognition; imaging; event related potentials. representation; brain Introduction Whether a pollster evaluating the sampling process for an election poll, a parishioner telling the time by counting the tolls of a church bell, or a child figuring out how much candy she had received on this Halloween versus a previous one, mental representations of numerical magnitude are important for projecting the future, monitoring the present, and learning from the past. Moreover, this ability to code our experiences numerically must scale consistently regardless of the shape, size, sensory modality or context in which particular numeric magnitudes are presented. Two prominent brain areas have been implicated in humans’ and other animals’ representation of numerical magnitudes: the prefrontal cortex and the horizontal segment of the intraparietal Sulcus (HIPS). Most studies have shown that HIPS plays a major role in numeric representation, with magnitude coded in this area as an abstract, notation-independent representation (Dehaene, Piazza, Pinel, Cohen, 2003; Dehaene, Dehaene-Lambertz, & Cohen, 1998; Libertus, Woldroff & Brannon, 2007). However, comparative and developmental studies have found HIPS playing a less prominent role. For example, single cell recordings in monkeys (Nieder & Merten, 2007 & Nieder & Miller, 2004) and fMRI studies in children (Ansari et al. 2005; Ansari & Dhital, 2006; Cantlon, Brannon, Carter & Pelphrey, 2006; Cantlon et al., 2009) have shown stronger effects of numerical magnitude on prefrontal cortex than HIPS. Similarly, ERP studies with infants, have also found that nonsymbolic numeric processing generates activity in a parieto-prefrontal network (Izard, Dehaene-Lambertz & Dehaene, 2008; Libertus, Pruitt, Woldorff & Brannon, 2009). To explain this developmental trend, we propose that: (1) at any given age, the brain represents numeric magnitudes using both a logarithmically-compressed code and a linear code, with the probability of a number being processed by the linear code increasing with age and experience; and (2) logarithmic-coding is predominantly processed in frontal areas, whereas linear coding is predominantly processed in parietal areas. Here we test an implication of this account, namely that large magnitude (low-frequency) numerals are more likely than small magnitude (high-frequency) numerals to be represented in frontal cortex, whereas the reverse is true of parietal cortex. Development of Numeric Representations The origin of our developmental hypothesis stems from behavioral studies on development of numeric representations (Booth & Siegler, 2006; Opfer & Siegler, 2007; Opfer & Thompson, 2008; Siegler & Opfer, 2003; Thompson & Opfer, 2008). In these studies, children and adults were asked to estimate the position of numbers on a blank line with the end-points labeled “0” and “100”, “0” and “1000”, or “0” and “10000”. This estimation task is particularly revealing about cognitive representations of numeric value because it transparently reflects the ratio characteristics of the number system. Overall, younger children’s estimates typically follow Fechner’s Law and