COGNITIVE NEUROSCIENCE Tuning to non-symbolic proportions in the human frontoparietal cortex Simon N. Jacob and Andreas Nieder Institute of Neurobiology, University of Tu ¨ bingen, Auf der Morgenstelle 28, 72076 Tu ¨ bingen, Germany Keywords: fMRI adaptation, human cerebral cortex, intraparietal sulcus, numerosity, proportions Abstract Humans share with many species a non-verbal system to estimate absolute quantity. This sense of number has been linked to the activity of quantity-selective neurons that respond maximally to preferred numerosities. With functional magnetic resonance imaging adaptation, we now show that populations of neurons in the human parietal and frontal cortex are also capable of encoding quantity ratios, or proportions, using the same non-verbal analog code as for absolute number. Following adaptation to visually presented constant proportions (specified by the ratio of line lengths or numerosities), we introduced novel relative magnitudes to examine the tuning characteristics of the population of stimulated neurons. In bilateral parietal and frontal cortex we found that blood oxygenation level-dependent signal recovery from adaptation was a function of numerical distance between the deviant proportion and the adaptation stimulus. The strongest effects were observed in the cortex surrounding the anterior intraparietal sulcus, a region considered pivotal for the processing of absolute magnitudes. Overall, there was substantial overlap of frontoparietal structures representing whole numbers and proportions. The identification of tuning to non-symbolic ratio stimuli, irrespective of notation, adds to the magnitude system a remarkable level of sophistication by demonstrating automatic access to a composite, derived quantitative measure. Our results argue that abstract concepts of both absolute and relative number are deeply rooted in the primate brain as fundamental determinants of higher-level numerical cognition. Introduction Grasping the concept of magnitude comes naturally to most species. Several lines of evidence indicate that our system to count, measure and rank items is phylogenetically ancient, evolving independently of language (Dehaene, 1997; Nieder, 2005). Simple enumeration or quantification, however, is often insufficient to make decisions and guide behavior. In many instances, we need to relate two quantities, generating a new composite construct: a proportion or magnitude ‘ratio’. Proportions are fundamental to mathematics and science, underlie the concept of percentage, and even govern seemingly subjective matters such as aesthetics and the sense of beauty (‘golden ratio’; Livio, 2002). Despite its paramount relevance for human culture, however, the neural underpinnings of proportional reasoning are largely unknown. To represent ratios accurately, humans exploit their symbolic numerical competence by using number fractions. A recent neuro- imaging study showed that fractions are represented by populations of neurons that are tuned to preferred ratios of numbers (Jacob & Nieder, 2009). Activity in the parietal cortex, more specifically in the intraparietal sulcus (IPS), a key region for the processing of absolute magnitude, was modulated as a function of the numerical distance of the presented from the preferred fraction. There were no differences in activation whether subjects viewed fraction numerals (e.g. 3 ⁄ 6) or fraction words (e.g. ‘half’) that were intermingled within a single experimental run. This insensitivity to stimulus notation indicates that fractions were encoded by their true numerical value and are not necessarily processed by numerator and denominator in separation. This strongly contrasts with common beliefs grounding on the fact that children and adults have considerable difficulties learning and using fractions (Bonato et al., 2007). The finding of cross-notation encoding of fractions raises the possibility of an abstract processor of magnitude ratios in the human IPS, and is strongly reminiscent of the system described for absolute numbers. Similar to absolute quantity, which can be judged approximately without symbols, proportion (relational quantity) can also be deter- mined non-verbally. Behavioral similarities are emerging between the non-symbolic representation of numerosities and proportions. For instance, infants can discriminate two ratios sufficiently far apart, long before the concept of proportionality is introduced during formal schooling (McCrink & Wynn, 2007). Electrophysiological recordings have shown that, in the monkey, single neurons respond to preferred non-symbolic proportions as described for absolute number (Vallentin & Nieder, 2008). Taken together, these observations suggest that quantity ratios are accessed automatically prior to the acquisition of language, possibly using cortical networks similar to those processing absolute quantity. However, a circuit to non-verbally represent magnitude ratios has not been described in humans. The identification of such a system would provide the much needed link between the infant and animal data on non-verbal proportions and the experiments addressing the processing of fractions (Jacob & Nieder, 2009). It could Correspondence: Dr S. N. Jacob, as above. E-mail: simon.jacob@biologie.uni-tuebingen.de Received 29 April 2009, revised 5 August 2009, accepted 8 August 2009 European Journal of Neuroscience, Vol. 30, pp. 1432–1442, 2009 doi:10.1111/j.1460-9568.2009.06932.x ª The Authors (2009). Journal Compilation ª Federation of European Neuroscience Societies and Blackwell Publishing Ltd European Journal of Neuroscience