Number sense " is a short-hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain-specific, biologically-determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology between the animal, infant, and human adult abilities for number processing ; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher-level cultural developments in arithmetic emerge through the establishment of linkages between this core analogical representation (the " number line ") and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution.

Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe...

INTRODUCTION How do we go from seeing a word to accessing its meaning? Classical models of word processing postulate that words are initially recognized in modalityspecific input lexicons before contacting a common semantic representation (Caramazza, 1996; Morton, 1979). This predicts that areas which are engaged in semantic-level processing should activate in direct correlation with the amount of semantic manipulation required by the task and do so independent of the modality of presentation of the concept (Chao et al., 2000; Perani et al., 1999; Vandenberghe et al., 1996). Here, we attempt to identify the cerebral areas engaged in the coding and internal manipulation of an abstract semantic content, the meaning of number words. Although numbers can be written in multiple notations, such as words or digits, the parietal lobes are thought to comprise a notation-independent representation of their semantic content as quantities. According to the "triple-code model" of number process

We measured cerebral activation with functional magnetic resonance imaging at 3 Tesla while eight healthy volunteers performed various number processing tasks known to be dissociable in brain-lesioned patients: naming, comparing, multiplying, or subtracting single digits. The results revealed the activation of a circuit comprising bilateral intraparietal, prefrontal, and anterior cingulate components. The extension and lateralization of this circuit was modulated by task demands. The intraparietal and prefrontal activation was more important in the right hemisphere during the comparison task and in the left hemisphere during the multiplication task and was intensely bilateral during the subtraction task. Thus, partially distinct cerebral circuits with the dorsal parietal pathway underlie distinct arithmetic operations.

The relative sparing of arabic numerals, in patients who failto read words or even letters, is a classical feature of pure alexla orlglnallyobserved by Dejerlne (Comptes Rendus des Seances de la Societé de la Biologie1892;4: 61-90).Wereport a study of number processlng abilities ln two patients sUfferlngfrom typical pure alexla. Our main flndlngwas that number Identificationperformance varled considerably wlthtask demands. Both patients could name pairs of digits, when they were engaged ln a simple namlng task or for the purpose of magnitude comparlson. ln contras " they frequently misldentifledthe very same digits when treating them as the components of multldlgltnumerals, or as the operands of addition problems. Withtwo-dlgitnumerals, a slmilar dissociation was shown between excellent comparison and severely impalred readlng aloud. Flnally,the variation of performance withtask demands was shown not to prevail withspelled-out numerals. These findings conflrm that some patients withpure alexla are able to process up to a semantic level symbolicstimuli that they cannot read aloud.Wespeculate that both hemispheres possess effective digit~dentiflcationabilitles, whlch are differenth:Ïlly called on depending on the task.

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Parsing a mental operation into components, characterizing the parallel or serial nature of this flow, and understanding what each process ultimately contributes to response time are fundamental questions in cognitive neuroscience. Here we show how a simple theoretical model leads to an extended set of predictions concerning the distribution of response time and its alteration by simultaneous performance of another task. The model provides a synthesis of psychological refractory period and random-walk models of response time. It merely assumes that a task consists of three consecutive stages—perception, decision based on noisy integration of evidence, and response—and that the perceptual and motor stages can operate simultaneously with stages of another task, while the central decision process constitutes a bottleneck. We designed a number-comparison task that provided a thorough test of the model by allowing independent variations in number notation, numerical distance, response complexity, and temporal asynchrony relative to an interfering probe task of tone discrimination. The results revealed a parsing of the comparison task in which each variable affects only one stage. Numerical distance affects the integration process, which is the only step that cannot proceed in parallel and has a major contribution to response time variability. The other stages, mapping the numeral to an internal quantity and executing the motor response, can be carried out in parallel with another task. Changing the duration of these processes has no significant effect on the variance. Citation: Sigman M, Dehaene S (2005) Parsing a cognitive task: A characterization of the mind’s bottleneck. PLoS Biol 3(2): e37.

Subjects classified visible 2-digit numbers as larger or smaller than 55. Target numbers were preceded by masked 2-digit primes that were either congruent (same relation to 55) or incongruent. Experiments 1 and 2 showed prime congruency effects for stimuli never included in the set of classified visible targets, indicating subliminal priming based on long-term semantic memory. Experiments 2 and 3 went further to demonstrate paradoxical unconscious priming effects resulting from task context. For example, after repeated practice classifying 73 as larger than 55, the novel masked prime 37 paradoxically facilitated the “larger ” response. In these experiments task context could induce subjects to unconsciously process only the leftmost masked prime digit, only the rightmost digit, or both independently. Across 3 experiments, subliminal priming was governed by both task context and long-term semantic memory. This research started by asking how much semantic analysis occurs unconsciously in response to visually masked numbers. Experiment 1 set out specifically to resolve a discrepancy between two recently reported findings. When it became apparent that Experiment 1’s methods could address additional interesting questions about subliminal priming, those additional questions became

Why is the human brain fundamentally limited when attempting to execute two tasks at the same time or in close succession? Two classical paradigms, psychological refractory period (PRP) and task switching, have independently approached this issue, making significant advances in our understanding of the architecture of cognition. Yet, there is an apparent contradiction between the conclusions derived from these two paradigms. The PRP paradigm, on the one hand, suggests that the simultaneous execution of two tasks is limited solely by a passive structural bottleneck in which the tasks are executed on a first-come, first-served basis. The task-switching paradigm, on the other hand, argues that switching back and forth between task configurations must be actively controlled by a central executive system (the system controlling voluntary, planned, and flexible action). Here we have explicitly designed an experiment mixing the essential ingredients of both paradigms: task uncertainty and task simultaneity. In addition to a central bottleneck, we obtain evidence for active processes of task setting (planning of the appropriate sequence of actions) and task disengaging (suppression of the plan set for the first task in order to proceed with the next one). Our results clarify the chronometric relations between these central components of dual-task processing, and in particular whether they operate serially or in parallel. On this basis, we propose a hierarchical model of cognitive architecture that provides a synthesis of task-switching and PRP paradigms.

INTRODUCTION The goal of the present work is to examine whether the semantic representations of numbers and body parts are associated with partially distinct cortical territories. Clinical and cognitive neuropsychology studies associate semantic deficits in both domains to lesions coarsely localized to the left parietal lobe (McCarthy and Warrington, 1990). Furthermore, patients with left inferior parietal lesions often exhibit simultaneous deficits for numbers and body parts (Benton, 1992; Gerstmann, 1940). Such an association of neuropsychological deficits is however notoriously ambiguous, and has been the subject of much debate. It might suggest that there is a shared substrate for numbers and body parts in the left parietal region, perhaps based on a common functional system for spatial representation and manipulation (Gerstmann, 1940) or on the crucial role that finger counting plays in numerical development (Butterworth, 1999). However, it might also reflect the existence of dis