A Magnitude Code Common to Numerosities and Number Symbols in Human Intraparietal Cortex

Numerical representation in the parietal lobes: abstract or not abstract?

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex.

Order and Magnitude Share a Common Representation in Parietal Cortex

The role of the intraparietal sulcus (IPS) in the representation of numerical magnitude is well established. Recently, there has also been speculation that the IPS is involved in the representation of ordinal information as well. These claims, however, overlook the fact that all neuroimaging paradigms in which participants make judgments about either magnitude and/or order result in a behavioral distance effect (i.e., the comparison is easier when the stimuli span a greater distance). This leaves open two possibilities: It may be that activation of the IPS is due to the mechanism that yields distance effects, or it may be that the IPS is involved in the representation of information about both magnitude and order. The current study used fMRI to compare a magnitude task in which participants show distance effects to an order-judgment task that yields reverse-distance effects. The results reveal activation of the IPS for both the magnitude and order tasks that is based on participants' strategies as opposed to the actual distance between the numbers. This leads to the conclusion that the IPS represents a mental number line, and that accessing this line can lead to distance effects when participants compare magnitudes and to reverse-distance effects when participants check for order.

The neural development of an abstract concept of number

As literate adults, we appreciate numerical values as abstract entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notation-independent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance imaging, we examine the brain mechanisms that 6- and 7-year-old children and adults recruit to solve numerical comparisons across different notation systems. The data reveal that when young children compare numerical values in symbolic and nonsymbolic notations, they invoke the same network of brain regions as adults including occipito-temporal and parietal cortex. However, children also recruit inferior frontal cortex during these numerical tasks to a much greater degree than adults. Our data lend additional support to an emerging consensus from adult neuroimaging, nonhuman primate neurophysiology, and computational modeling studies that a core neural system integrates notation-independent numerical representations throughout development but, early in development, higher-order brain mechanisms mediate this process.

Representation of number in the brain

Number symbols have allowed humans to develop superior mathematical skills that are a hallmark of technologically advanced cultures. Findings in animal cognition, developmental psychology, and anthropology indicate that these numerical skills are rooted in nonlinguistic biological primitives. Recent studies in human and nonhuman primates using a broad range of methodologies provide evidence that numerical information is represented and processed by regions of the prefrontal and posterior parietal lobes, with the intraparietal sulcus as a key node for the representation of the semantic aspect of numerical quantity.

Where syntax meets math: right intraparietal sulcus activation in response to grammatical number agreement violations

Previous research has shown that the processing of words referring to actions activated motor areas. Here, we show activation of the right intraparietal sulcus, an area that has been associated with quantity processing, when participants are asked to read pairs of words with number agreement violations as opposed to phrases with gender agreement violations or with no violation. In addition, we show activation in the left premotor and left inferior frontal areas when either gender or number agreement is violated. We argue that number violation automatically activates processes linked to quantity processing which are not directly related to language mechanisms.

The role of the anterior temporal lobes in the comprehension of concrete and abstract words: rTMS evidence

Conceptual knowledge allows us to bring meaning to our world. Studies of semantic dementia (SD) patients and some functional neuroimaging studies indicate that the anterior temporal lobes, bilaterally, are a core neural substrate for the formation of conceptual representations. The majority of SD patients (who have circumscribed atrophy of the anterior temporal lobes) have better comprehension of concrete than abstract words. However, this finding remains controversial, as some individual SD patients have exhibited reverse imageability effects, i.e., relative preservation of abstract knowledge. This would imply that the anterior temporal lobes are particularly crucial for processing sensory aspects of semantic knowledge, which are an important part of concrete but not abstract concepts. To adjudicate on this debate, we used offline, low-frequency, repetitive transcranial magnetic stimulation to disrupt neural processing temporarily in the left or right temporal poles (TPs). We examined this effect using a synonym judgement task, comprising high, medium and low imageability items, which we have previously employed with a case-series of SD patients. The time required to make semantic decisions was slowed considerably, particularly for low imageability items, consistent with the pattern we observed in SD. These results confirm that both TPs make a critical contribution to semantic processing, even for abstract concepts that do not have strong sensory representations.

Common and specific contributions of the intraparietal sulci to numerosity and length processing

Numerical and spatial magnitude processing have long been intimately associated, leading to the suggestion that they share a common system of magnitude representation. Although separate investigations on the cerebral areas involved in numerosity and spatial estimation point toward the parietal cortex, the precise anatomical overlap, if any, has not yet been directly established. Here, functional magnetic resonance imaging was used to localize the cerebral network involved in processing both numerosity and length. Blood oxygenation level-dependent signal changes were measured while healthy volunteers were making numerosity comparisons on linear arrays of dots, and length comparisons on discrete linear arrays of dots and continuous rectangles. The results show the bilateral involvement of parietal regions around the intraparietal sulci in explicit and implicit processing of numerosity, and a right lateralized occipitoparietal network activation in length processing; numerosity and length processing both activate the right IPS and the precentral gyrus. By excluding the mandatory intrinsic spatial processing of arrays, we demonstrate that the left IPS is involved in numerosity processing only, whereas the right IPS underlies a common processing mechanism or representation of spatial and numerical magnitude.

The Cerebral Basis of Mapping Nonsymbolic Numerical Quantities onto Abstract Symbols: An fMRI Training Study

Although significant insights into the neural basis of numerical and mathematical processing have been made, the neural processes that enable abstract symbols to become numerical remain largely unexplored in humans. In the present study, adult participants were trained to associate novel symbols with nonsymbolic numerical magnitudes (arrays of dots). Functional magnetic resonance imaging was used to examine the neural correlates of numerical comparison versus recognition of the novel symbols after each of two training stages. A left-lateralized fronto-parietal network, including the intraparietal sulcus, the precuneus, and the dorsal prefrontal cortex, was more active during numerical comparison than during perceptual recognition. In contrast, a network including bilateral temporal–occipital regions was more active during recognition than comparison. A whole-brain three-way interaction revealed that those individuals who had higher scores on a postscan numerical task (measuring their understanding of the global numerical organization of the novel symbols) exhibited increasing segregation between the two tasks in the bilateral intraparietal sulci as a function of increased training. Furthermore, whole-brain regression analysis showed that activity in the left intraparietal sulcus was systematically related to the effect of numerical distance on accuracy. These data provide converging evidence that parietal and left prefrontal cortices are involved in learning to map numerical quantities onto visual symbols. Only the parietal cortex, however, appeared systematically related to the degree to which individuals learned to associate novel symbols with their numerical referents. We conclude that the left parietal cortex, in particular, may play a central role in imbuing visual symbols with numerical meaning.

The case for a notation-independent representation of number

Cohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W's prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.

Beyond format-specificity: Is analogue magnitude really the core abstract feature of the cultural number representation?

The issue of abstractness raises two distinct questions. First, is there a format-independent magnitude representation? Second, does analogue magnitude really play a crucial role in the development of human mathematics? We suggest that neither developmental nor cultural studies support this notion. The field needs to redefine the properties of the core number representation as used in human arithmetic.

All numbers are not equal: an electrophysiological investigation of small and large number representations

Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small numbers of objects. To investigate neural signatures of this distinction, event-related potentials were recorded as adult humans passively viewed the sequential presentation of dot arrays in an adaptation paradigm. In two studies, subjects viewed successive arrays of a single number of dots interspersed with test arrays presenting the same or a different number; numerical range (small numerical quantities 1-3 vs. large numerical quantities 8-24) and ratio difference varied across blocks as continuous variables were controlled. An early-evoked component (N1), observed over widespread posterior scalp locations, was modulated by absolute number with small, but not large, number arrays. In contrast, a later component (P2p), observed over the same scalp locations, was modulated by the ratio difference between arrays for large, but not small, numbers. Despite many years of experience with symbolic systems that apply equally to all numbers, adults spontaneously process small and large numbers differently. They appear to treat small-number arrays as individual objects to be tracked through space and time, and large-number arrays as cardinal values to be compared and manipulated.

Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: an fMRI study

Numbers are everywhere in modern life. Looking out a window, one might see both symbolic numbers, like the numerals on a thermometer, and nonsymbolic quantities, such as the number of chickadees at a bird feeder. Although differences between symbolic and nonsymbolic numbers appear very salient, most research on numerical cognition has focused on similarities rather than differences between numerical stimulus formats. Thus, little is known about differences in the processing of symbolic and nonsymbolic numerical magnitudes. A recent computational model proposed that symbolic and nonsymbolic quantities undergo distinct encoding processes which then converge on a common neural representation of numerical magnitude (Verguts, T., Fias, W., 2004. Representation of number in animals and humans: a neural model. J. Cogn. Neurosci. 16 (9), 1493-1504.). Moreover, this model predicted that discrete brain regions underlie these encoding processes. Using functional magnetic resonance imaging, the present study tested the predictions of this model by examining the functional neuroanatomy of symbolic and nonsymbolic number processing. Nineteen adults compared the relative numerical magnitude of symbolic and nonsymbolic stimuli. An initial conjunction analysis revealed the right inferior parietal lobule to be significantly active in both symbolic and nonsymbolic numerical comparison. A contrast of the activation associated with symbolic and nonsymbolic stimuli revealed that both the left angular and superior temporal gyri were more activated for symbolic compared to nonsymbolic numerical magnitude judgments. The reverse comparison (nonsymbolic>symbolic) revealed several regions including the right posterior superior parietal lobe. These results reveal both format-general and format-specific processing of numerical stimuli in the brain. The potential roles of these regions in symbolic and nonsymbolic numerical processing are discussed.

Non-abstract numerical representations in the IPS: Further support, challenges, and clarifications

The commentators have raised many pertinent points that allow us to refine and clarify our view. We classify our response comments into seven sections: automaticity; developmental and educational questions; priming; multiple representations or multiple access(?); terminology; methodological advances; and simulated cognition and numerical cognition. We conclude that the default numerical representations are not abstract.

What is an (abstract) neural representation of quantity?

We argue that Cohen Kadosh & Walsh's (CK&W's) definitions of neural coding and of abstract representations are overly shallow, influenced by classical cognitive psychology views of modularity and seriality of information processing, and incompatible with the current knowledge on principles of neural coding. As they stand, the proposed dichotomies are not very useful heuristic tools to guide our research towards a better understanding of the neural computations underlying the processing of numerical quantity in the parietal cortex.

Mathematical skills in Williams syndrome: insight into the importance of underlying representations

Williams syndrome (WS) is a developmental disorder characterized by relatively spared verbal skills and severe visuospatial deficits. Serious impairments in mathematics have also been reported. This article reviews the evidence on mathematical ability in WS, focusing on the integrity and developmental path of two fundamental representations, namely those that support judgments of "how much" (i.e., magnitude) and "how many" (i.e., number of objects). Studies on magnitude or "number line" representation in WS suggest that this core aspect of mathematical ability, is atypical in WS throughout development, causing differences on some but not all aspects of math. Studies on the representation of small numbers of objects in WS are also reviewed, given the proposed links between this type of representation and early number skills such as counting. In WS, representation appears to be relatively typical in infancy but limitations become evident by maturity, suggesting a truncated developmental trajectory. The math deficits in WS are consistent with neurological data indicating decreased gray matter and hypoactivation in parietal areas in WS, as these areas are implicated in mathematical processing as well as visuospatial abilities and visual attention. In spite of their deficits in core mathematical representations, people with WS can learn many mathematical skills and show some strengths, such as reading numbers. Thus individuals with WS may be able to take advantage of their relatively strong verbal skills when learning some mathematical tasks. The uneven mathematical abilities found in persons with WS provide insight into not only appropriate remediation for this developmental disorder but also into the precursors of mathematical ability, their neural substrates, and their developmental importance.

Newborn infants perceive abstract numbers

Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4-18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience.

Quantity without numbers and numbers without quantity in the parietal cortex

A dominant view in numerical cognition is that processing the quantity indicated by numbers (e.g. deciding the larger between two numbers such as '12.07' or '15.02') relies on the intraparietal regions (IPS) of the cerebral cortex. However, it remains unclear whether the IPS could play a more general role in numerical cognition, for example in (1) quantity processing even with non-numerical stimuli (e.g. choosing the larger of 'bikini' and 'coat'); and/or (2) conceptual tasks involving numbers beyond those requiring quantity processing (e.g. attributing a summer date to either '12.07' or '15.02'). In this study we applied fMRI-guided TMS to the left and right IPS, while independently manipulating stimulus and task. Our results showed that IPS involvement in numerical cognition is neither stimulus-specific nor specific for conceptual tasks. Thus, quantity judgments with numerical and non-numerical stimuli were equally affected by IPS-TMS, as well as a number conceptual task not requiring quantity comparisons. However, IPS-TMS showed no impairment for perceptual decisions on numbers without any conceptual processing (i.e. colour judgment), nor for conceptual decisions that did not involve quantity or number stimuli (e.g. summer object: 'bikini' or 'coat'?). These results are consistent with proposals that the parietal areas are engaged in the conceptual representation of numbers but they challenge the most common view that number processing is so automatic that the simple presentation of numbers activates the IPS and a sense of magnitude. Rather, our results show that the IPS is only necessary when conceptual operations need to be explicitly oriented to numerical concepts.

Neural correlates of depth of strategic reasoning in medial prefrontal cortex

We used functional MRI (fMRI) to investigate human mental processes in a competitive interactive setting--the "beauty contest" game. This game is well-suited for investigating whether and how a player's mental processing incorporates the thinking process of others in strategic reasoning. We apply a cognitive hierarchy model to classify subject's choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. According to this model, high-level reasoners expect the others to behave strategically, whereas low-level reasoners choose based on the expectation that others will choose randomly. The data show that high-level reasoning and a measure of strategic IQ (related to winning in the game) correlate with the neural activity in the medial prefrontal cortex, demonstrating its crucial role in successful mentalizing. This supports a cognitive hierarchy model of human brain and behavior.

Prefrontal cortex and the evolution of symbolic reference

Symbol systems such as numbers and language are of paramount importance to human cognition. In number theory, numbers are symbolic signs embedded in a system of higher-order sign-sign relations. During ontogeny, numerical competence passes through different referential sign relations with increasing complexity, from an iconic to an indexical and finally symbolic stage. Animals such as nonhuman primates are constrained to indexical reference. However, because symbolic reference emerges from indexical reference, behavioral and neuronal representations of semantic sign-numerosity associations in animals can elucidate the precursors of symbol systems. A neurobiological explanation of how numerical signs take their meaning is proposed by suggesting that neurons in the granular prefrontal cortex, a novel brain structure evolved in primates, enable high-order associations and establish links between nonsymbolic numerosities and arbitrary signs.

How Humans Count: Numerosity and the Parietal Cortex

Numerosity (the number of objects in a set), like color or movement, is a basic property of the environment. Animal and human brains have been endowed by evolution by mechanisms based on parietal circuitry for representing numerosity in an highly abstract, although approximate fashion. These mechanisms are functional at a very early age in humans and spontaneously deployed in the wild by animals of different species. The recent years have witnessed terrific advances in unveiling the neural code(s) underlying numerosity representations and showing similarities as well as differences across species. In humans, during development, with the introduction of symbols for numbers and the implementation of the counting routines, the parietal system undergoes profound (yet still largely mysterious) modifications, such that the neural machinery previously evolved to represent approximate numerosity gets partially “recycled” to support the representation of exact number.

Notation-independent representation of fractions in the human parietal cortex

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.

Functional heterogeneity of inferior parietal cortex during mathematical cognition assessed with cytoarchitectonic probability maps

Although the inferior parietal cortex (IPC) has been consistently implicated in mathematical cognition, the functional roles of its subdivisions are poorly understood. We address this problem using probabilistic cytoarchitectonic maps of IPC subdivisions intraparietal sulcus (IPS), angular gyrus (AG), and supramarginal gyrus. We quantified IPC responses relative to task difficulty and individual differences in task proficiency during mental arithmetic (MA) tasks performed with Arabic (MA-A) and Roman (MA-R) numerals. The 2 tasks showed similar levels of activation in 3 distinct IPS areas, hIP1, hIP2, and hIP3, suggesting their obligatory role in MA. Both AG areas, PGa and PGp, were strongly deactivated in both tasks, with stronger deactivations in posterior area PGp. Compared with the more difficult MA-R task, the MA-A task showed greater responses in both AG areas, but this effect was driven by less deactivation in the MA-A task. AG deactivations showed prominent overlap with lateral parietal nodes of the default mode network, suggesting a nonspecific role in MA. In both tasks, greater bilateral AG deactivation was associated with poorer performance. Our findings suggest a close link between IPC structure and function and they provide new evidence for behaviorally salient functional heterogeneity within the IPC during mathematical cognition.

Origins of mathematical intuitions: the case of arithmetic

Mathematicians frequently evoke their "intuition" when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of "core knowledge" associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.

The processing and representation of fractions within the brain: an fMRI investigation

Little is known about how adults process fractions and how fractions are represented in the brain. The intraparietal sulcus is assumed to host an analogue representation of number magnitude. It is unknown, however, how the magnitude of fractions is represented in the brain. Fraction magnitude might be represented by the numerical value of the fraction as a whole or might involve separate representations of the values of the fractions' denominator and numerator. The present fMRI study investigated brain areas involved in fraction comparison. As a diagnostic for fraction processing, the numerical distance effect (reaction times and error rates increase as the distance between the numbers being compared decreases) was evaluated. If fractions are represented as their numerical value, a distance effect is expected for the distance between the numerical values of the two fractions being compared. If fractions are represented in parts, however, that is, as the separate values of their denominators and numerators, a distance effect is expected for the distances between the two fractions' numerators and denominators, respectively. Although both types of distance effects were observed in the behavioral data, only the distance between the numerical values of the two fractions was observed to modulate activation within the intraparietal sulcus (IPS). This indicates that, within the IPS, a fraction might be represented by its numerical value as a whole, rather than by the numerical values of its numerator and denominator.

Contributions of primate prefrontal and posterior parietal cortices to length and numerosity representation

The ability to understand and manipulate quantities ensures the survival of animals and humans alike. The frontoparietal network in primates has been implicated in representing, along with other cognitive abilities, abstract quantity. The respective roles of the prefrontal and parietal areas and the way continuous quantities, as opposed to discrete ones, are represented in this network, however, are unknown. We investigated this issue by simultaneously analyzing recorded single-unit activity in the prefrontal cortex (PFC) and the fundus of the intraparietal sulcus (IPS) of two macaque monkeys while they were engaged in delayed match-to-sample tasks discriminating line length and numerosity. In both areas, we found anatomically intermingled neurons encoding either length, numerosity, or both types of quantities. Even though different sets of neurons coded these quantities, the representation of length and numerosity was similar within the IPS and PFC. Both length and numerosity were coded by tuning functions peaking at the preferred quantity, thus supporting a labeled-line code for continuous and discrete quantity. A comparison of the response characteristics between parietal and frontal areas revealed a larger proportion of IPS neurons representing each quantity type in the early sample phase, in addition to shorter response latencies to quantity for IPS neurons. Moreover, IPS neurons discriminated quantities during the sample phase better than PFC neurons, as quantified by the receiver operating characteristic area. In the memory period, the discharge properties of PFC and IPS neurons were comparable. These single-cell results are in good agreement with functional imaging data from humans and support the notion that representations of continuous and discrete quantities share a frontoparietal substrate, with IPS neurons constituting the putative entry stage of the processing hierarchy.

Neuroscience of learning arithmetic--evidence from brain imaging studies

It is widely accepted that the human brain is remarkably adaptive not only in child development, but also during adulthood. Aim of this work is to offer an overview and a systematic analysis of neuroimaging studies on the acquisition of arithmetic expertise. In normally developing children and adults, the gain of arithmetic competence is reflected by a shift of activation from frontal brain areas to parietal areas relevant for arithmetic processing. A shift of activation is also observed within the parietal lobe from the intraparietal sulci to the left angular gyrus. Increases in angular gyrus activation with gaining of expertise have also been documented in other cognitive domains. It appears that the left angular gyrus activation is modulated by inter-individual differences in arithmetic performance. The comparison of normal individuals with exceptionally performing individuals (e.g., calculating prodigies) suggests that the experts' arithmetic proficiency relies on a more extended activation network than the network found in non-experts. In expert individuals with long-lasting, extensive mathematical training, specific structural brain modifications are also evident.

Brain correlates of non-symbolic numerosity estimation in low and high mathematical ability children

Previous studies have implicated several brain areas as subserving numerical approximation. Most studies have examined brain correlates of adult numerical approximation and have not considered individual differences in mathematical ability. The present study examined non-symbolic numerical approximation in two groups of 10-year-olds: Children with low and high mathematical ability. The aims of this study were to investigate the brain mechanisms associated with approximate numerosity in children and to assess whether individual differences in mathematical ability are associated with differential brain correlates during the approximation task. The results suggest that, similarly to adults, multiple and distributed brain areas are involved in approximation in children. Despite equal behavioral performance, there were differences in the brain activation patterns between low and high mathematical ability groups during the approximation task. This suggests that individual differences in mathematical ability are reflected in differential brain response during approximation.

Social distance evaluation in human parietal cortex

Across cultures, social relationships are often thought of, described, and acted out in terms of physical space (e.g. “close friends” “high lord”). Does this cognitive mapping of social concepts arise from shared brain resources for processing social and physical relationships? Using fMRI, we found that the tasks of evaluating social compatibility and of evaluating physical distances engage a common brain substrate in the parietal cortex. The present study shows the possibility of an analytic brain mechanism to process and represent complex networks of social relationships. Given parietal cortex's known role in constructing egocentric maps of physical space, our present findings may help to explain the linguistic, psychological and behavioural links between social and physical space.

Spontaneous mapping of number and space in adults and young children

Mature representations of space and number are connected to one another in ways suggestive of a 'mental number line', but this mapping could either be a cultural construction or a reflection of a more fundamental link between the domains of number and geometry. Using a manual bisection paradigm, we tested for number line representations in adults, young school children, and preschool children. Non-symbolic numerical displays systematically distorted localization of the midpoint of a horizontal line at all three ages. Numerical and spatial representations therefore are linked prior to the onset of formal instruction, in a manner that suggests a privileged relation between spatial and numerical cognition.

Beyond the number domain

In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. Here, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain - a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory and its physical instantiation in the brain.

An investigation of the effects of relative probability of old and new test items on the neural correlates of successful and unsuccessful source memory

The present event-related fMRI study addressed the question whether retrieval-related neural activity in lateral parietal cortex is affected by the relative probability of test items. We varied the proportion of old to new items across two test blocks, with 25% of the items being old in one block and 75% being old in the other. Prior to each block, participants (N=18) completed one of two types of study judgment on each of 108 object images. They then performed a source memory test with four response options: studied in task 1, studied in task 2, old but unsure of the study task, and new. Retrieval-related activity in regions previously identified as recollection-sensitive, including the left inferior lateral parietal cortex and bilateral medial temporal cortex, was unaffected by old/new ratio. Generic retrieval success effects--retrieval-related effects common to recognized items attracting either a correct or an incorrect source judgment--were identified in several regions of left superior parietal cortex. These effects dissociated between a middle region of the intraparietal sulcus (IPS), where activity did not interact with ratio, and regions anterior and posterior to the middle IPS where activity was sensitive to old/new ratio. The findings are inconsistent with prior proposals that retrieval-related activity in and around the left middle IPS reflects the relative salience of old and new test items. Rather, they suggest that, as in the case of more inferior left parietal regions, retrieval-related activity in this region reflects processes directly linked to retrieval.