Notation-Independent Representation of Fractions in the Human Parietal Cortex

Abstract

Although the concept of whole numbers is intuitive and well suited for counting and ordering, it is with the invention of fractions that the number system gained precision and flexibility. Absolute magnitude is encoded by single neurons that discharge maximally to specific numbers. However, it is unknown how the ratio of two numbers is represented, whether by processing numerator and denominator in separation, or by extending the analog magnitude code to relative quantity. Using functional MRI adaptation, we now show that populations of neurons in human fronto-parietal cortex are tuned to preferred fractions, generalizing across the format of presentation. After blood oxygen level-dependent signal adaptation to constant fractions, signal recovery to deviant fractions was modulated parametrically as a function of numerical distance between the deviant and adaptation fraction. The distance effect was invariant to changes in notation from number to word fractions and strongest in the anterior intraparietal sulcus, a key region for the processing of whole numbers. These findings demonstrate that the human brain uses the same analog magnitude code to represent both absolute and relative quantity. Our results have implications for mathematical education, which may be tailored to better harness our ability to access automatically a composite quantitative measure.

Neural representations of magnitude for natural and rational numbers

“…To date, these alternative predictions remain untested. In fact, only two studies have ever probed the neural representations underlying the processing of fractional numbers (Ishebeck et al, 2009;Jacob and Nieder, 2009a), and neither of these assessed the neural representations underlying decimal numbers, or the relationship between neural representations of magnitude across different formats for rational numbers.…”

“…Jacob and Nieder (2009a) used an adaptation paradigm to test symbolic fraction magnitudes (single and multi-digit fractions). Recovery in the BOLD signal after habituation was observed in the frontoparietal cortex, and specifically the IPS.…”

Cross-Format Physical Similarity Effects and Their Implications for the Numerical Cognition Architecture

“…For example, using an fMRI, Piazza, Izard, Pinel, Bihan, and Dehaene (2004) demonstrated that different symbolic formats activate an abstract quantity representation in the hIPS. In addition, fMRI research has also found that multiple numerical formats activate the same IPS area (Jacob & Nieder, 2009;Piazza, Pinel, Bihan, & Dehaene, 2007). In contrast, fMRI research has found that quantity representations appear to be format dependent in both the left (Cohen Kadosh, Muggleton, Silvanto, & Walsh, 2010;Cohen Kadosh et al, 2007) and right (Cohen Kadosh et al, 2010) parietal lobes.…”

Supramodal numerosity selectivity of neurons in primate prefrontal and posterior parietal cortices

“…Studies with behaviorally trained monkeys have identified a parieto-frontal network of individual neurons selectively tuned to the number of items. This cortical network is putatively homologous with the network endowing humans to estimate numerosity, count, and operate with number symbols (5)(6)(7)(8)(9)(10)(11)(12).…”