Exact and approximate judgements of visual and auditory numerosity: An fMRI study

Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation

The main aim of the present coordinate-based meta-analysis is to identify brain regions that are commonly activated in functional magnetic resonance imaging studies (fMRI) investigating number processing and calculation in children. Here, we include 19 developmental fMRI papers, five of which also examine children diagnosed with developmental dyscalculia and/or mathematical disability. Results reveal that children produce consistent fronto-parietal activation patterns in response to number processing and calculation. Importantly, activation patterns are clearly modulated by notation, task complexity, and competence level. Activation differences between children with and without dyscalculia are observable in number-relevant parietal regions as well as in (pre)frontal and occipital cortex.

Some is not enough: quantifier comprehension in corticobasal syndrome and behavioral variant frontotemporal dementia

Quantifiers are very common in everyday speech, but we know little about their cognitive basis or neural representation. The present study examined comprehension of three classes of quantifiers that depend on different cognitive components in patients with focal neurodegenerative diseases. Patients evaluated the truth-value of a sentence containing a quantifier relative to a picture illustrating a small number of familiar objects, and performance was related to MRI grey matter atrophy using voxel-based morphometry. We found that patients with corticobasal syndrome (CBS) and posterior cortical atrophy (PCA) are significantly impaired in their comprehension of cardinal quantifiers (e.g. "At least three birds are on the branch"), due in part to their deficit in quantity knowledge. MRI analyses related this deficit to temporal-parietal atrophy found in CBS/PCA. We also found that patients with behavioral variant frontotemporal dementia (bvFTD) are significantly impaired in their comprehension of logical quantifiers (e.g. "Some of the birds are on the branch"), associated with a simple form of perceptual logic, and this correlated with their deficit on executive measures. This deficit was related to disease in rostral prefrontal cortex in bvFTD. These patients were also impaired in their comprehension of majority quantifiers (e.g. "At least half of the birds are on the branch"), and this too was correlated with their deficit on executive measures. This was related to disease in the basal ganglia interrupting a frontal-striatal loop critical for executive functioning. These findings suggest that a large-scale frontal-parietal neural network plays a crucial role in quantifier comprehension, and that comprehension of specific classes of quantifiers may be selectively impaired in patients with focal neurodegenerative conditions in these areas.

Functional specificity for high-level linguistic processing in the human brain

Neuroscientists have debated for centuries whether some regions of the human brain are selectively engaged in specific high-level mental functions or whether, instead, cognition is implemented in multifunctional brain regions. For the critical case of language, conflicting answers arise from the neuropsychological literature, which features striking dissociations between deficits in linguistic and nonlinguistic abilities, vs. the neuroimaging literature, which has argued for overlap between activations for linguistic and nonlinguistic processes, including arithmetic, domain general abilities like cognitive control, and music. Here, we use functional MRI to define classic language regions functionally in each subject individually and then examine the response of these regions to the nonlinguistic functions most commonly argued to engage these regions: arithmetic, working memory, cognitive control, and music. We find little or no response in language regions to these nonlinguistic functions. These data support a clear distinction between language and other cognitive processes, resolving the prior conflict between the neuropsychological and neuroimaging literatures.

Comparison of quantities: core and format-dependent regions as revealed by fMRI

The perception and handling of numbers is central to education. Numerous imaging studies have focused on how quantities are encoded in the brain. Yet, only a few studies have touched upon number mining: the ability to extract the magnitude encoded in a visual stimulus. This article aims to characterize how analogue (i.e., disks and dots) and symbolic (i.e., positive and negative integers) formats influence number mining and the representation of quantities. Sixteen adult volunteers completed a comparison task while we recorded the blood oxygen level-dependent response using functional magnetic resonance imaging. The results revealed that a restricted set of specific subdivisions in the right intraparietal sulcus is activated in all conditions. With respect to magnitude assessment, the results show that 1) analogue stimuli are predominantly processed in the right hemisphere and that 2) symbolic stimuli encompass the analogue system and further recruit areas in the left hemisphere. Crucially, we found that polarity is encoded independently from magnitude. We refine the triple-code model by integrating our findings.

A common right fronto-parietal network for numerosity and duration processing: an fMRI study

Numerosity and duration processing have been modeled by a functional mechanism taking the form of an accumulator working under two different operative modes. Separate investigations of their cerebral substrates have revealed partly similar patterns of activation, mainly in parietal and frontal areas. However, the precise cerebral implementation of the accumulator model within these areas has not yet been directly assessed. In this study, we asked participants to categorize the numerosity of flashed dot sequences or the duration of single dot displays, and we used functional magnetic resonance imaging (fMRI) to examine the common neural correlates of these processes. The results reveal a large right-lateralized fronto-parietal network, including the intraparietal sulcus (IPS) and areas in the precentral, middle and superior frontal gyri, which is activated by both numerosity and duration processing. Complementary psychophysiological interaction (PPI) analyses show a functional connectivity between the right IPS and the frontal areas in both tasks, whereas the right IPS was functionally connected to the left IPS and the right precentral area in the numerosity categorization task only. We propose that the right IPS underlies a common magnitude processing system for both numerosity and duration, possibly corresponding to the encoding and accumulation stages of the accumulator model, whereas the frontal areas are involved in subsequent working-memory storage and decision-making processes.

Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

Role of distinct parietal areas in arithmetic: an fMRI-guided TMS study

Although several parietal areas are known to be involved in number processing, their possible role in arithmetic operations remains debated. It has been hypothesized that the horizontal segment of the intraparietal sulcus (hIPS) and the posterior superior parietal lobule (PSPL) contribute to operations solved by calculation procedures, such as subtraction, but whether these areas are also involved in operations solved by memory retrieval, such as multiplication, is controversial. In the present study, we first identified the parietal areas involved in subtraction and multiplication by means of functional magnetic resonance imaging (fMRI) and we found an increased activation, bilaterally, in the hIPS and PSPL during both arithmetic operations. In order to test whether these areas are causally involved in subtraction and multiplication, we used transcranial magnetic stimulation (TMS) to create, in each participant, a virtual lesion of either the hIPS or PSPL, over the sites corresponding to the peaks of activation gathered in fMRI. When compared to a control site, we found an increase in response latencies in both operations after a virtual lesion of either the left or right hIPS, but not of the PSPL. Moreover, TMS over the hIPS increased the error rate in the multiplication task. The present results indicate that even operations solved by memory retrieval, such as multiplication, rely on the hIPS. In contrast, the PSPL seems to underlie processes that are nonessential to solve basic subtraction and multiplication problems.

Beyond hemispheric dominance: brain regions underlying the joint lateralization of language and arithmetic to the left hemisphere

Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific cerebral subregions? Or is it merely coincidental? To shed light on this issue, we performed a "colateralization analysis" over 209 healthy subjects: We investigated whether normal variations in the degree of left hemispheric asymmetry in areas involved in sentence listening and reading are mirrored in the asymmetry of areas involved in mental arithmetic. Within the language network, a region-of-interest analysis disclosed partially dissociated patterns of lateralization, inconsistent with an overall "dominance" model. Only two of these areas presented a lateralization during sentence listening and reading which correlated strongly with the lateralization of two regions active during calculation. Specifically, the profile of asymmetry in the posterior superior temporal sulcus during sentence processing covaried with the asymmetry of calculation-induced activation in the intraparietal sulcus, and a similar colateralization linked the middle frontal gyrus with the superior posterior parietal lobule. Given recent neuroimaging results suggesting a late emergence of hemispheric asymmetries for symbolic arithmetic during childhood, we speculate that these colateralizations might constitute developmental traces of how the acquisition of linguistic symbols affects the cerebral organization of the arithmetic network.

The perceptual expansion of a filled area depends on textural characteristics

According to the Oppel-Kundt illusion, a filled space appears larger than an empty one. In the present research we studied how textural characteristics affect the perceived size of two-dimensional patterns. We investigated the perceived extension of square textures by manipulating spatial frequency and filling microelements' numerosity. Subjects compared the test stimuli with a uniform gray square varied in size and performed the task both with the adjustment and the constant stimuli methods. An illusory increment of area extension was generally found with textured stimuli. The illusory effect increased with spatial frequency and decreased with the microelements' number, indicating an independent processing of these two basic properties. Moreover, the smaller effect found when spatial frequency extraction became harder, confirmed that the illusion involves spatial frequency processing. Finally, the reduced overestimation of areas observed with a weaker subparts' articulation confirmed the relevance of clear distinguishable micropatterns at the basis of the phenomenon. Those results demonstrate the influence of textural statistical properties on perceiving the size of a visual object.

Understanding quantity in semantic dementia

Patients with semantic dementia (SD) show relative preservation of number skills, contrasting with their severe multimodal semantic impairment. Underpinning this preservation, it is argued, is spared understanding of numerical quantity, a competence likened to a spatial map and subserved by the parietal lobes. The study investigated quantity knowledge in 14 SD patients to determine whether it is consistently preserved irrespective of disease severity or whether there are constraints on this preserved knowledge domain. Performance was well preserved on Piagetian conservation tasks, estimating object numerosity, and understanding of basic numerical magnitude. However, patients showed impairment on real-world estimation tasks, increasing with semantic severity. More surprisingly, on an analogue scale task, they produced implausible responses, suggesting degraded knowledge of precise numerical relationships. The findings challenge the view that knowledge of quantity is totally preserved in SD and suggest that the temporal lobes have a contributory role in the conceptual understanding of quantity.

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.

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.

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.

One, two, three, many - subitizing in active touch

'Subitizing' refers to rapid and accurate judgement of small numbers of items, while response times and error rates increase rapidly for larger set-sizes. Most enumeration studies have been done in vision. Enumeration studies in touch have mostly involved 'passive touch', i.e. touch without active exploration. In daily life a much more common situation is that of 'active touch', e.g. when we count the number of coins in our pocket. To investigate numerosity judgement in active touch, we let subjects haptically explore varying numbers of spheres. Our results show that enumeration for up to 3 items is more efficient than for larger numbers of items. We also show that enumeration in this regime was not performed through estimation. Furthermore, it is shown that numerosity information was accessed directly and not through mass or volume cues. Not only do our results show that a haptic version of subitizing exists in active touch, they also suggest similar underlying enumeration mechanisms across different modalities.

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.

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.

Developmental changes in category-specific brain responses to numbers and letters in a working memory task

Neuroimaging studies have identified a common network of brain regions involving the prefrontal and parietal cortices across a variety of working memory (WM) tasks. However, previous studies have also reported category-specific dissociations of activation within this network. In this study, we investigated the development of category-specific activation in a WM task with digits, letters, and faces. Eight-year-old children and adults performed a 2-back WM task while their brain activity was measured using functional magnetic resonance imaging (fMRI). Overall, children were significantly slower and less accurate than adults on all three WM conditions (digits, letters, and faces); however, within each age group, behavioral performance across the three conditions was very similar. FMRI results revealed category-specific activation in adults but not children in the intraparietal sulcus for the digit condition. Likewise, during the letter condition, category-specific activation was observed in adults but not children in the left occipital-temporal cortex. In contrast, children and adults showed highly similar brain-activity patterns in the lateral fusiform gyri when solving the 2-back WM task with face stimuli. Our results suggest that 8-year-old children do not yet engage the typical brain regions that have been associated with abstract or semantic processing of numerical symbols and letters when these processes are task-irrelevant and the primary task is demanding. Nevertheless, brain activity in letter-responsive areas predicted children's spelling performance underscoring the relationship between abstract processing of letters and linguistic abilities. Lastly, behavioral performance on the WM task was predictive of math and language abilities highlighting the connection between WM and other cognitive abilities in development.

Neural correlates of approximate quantification strategies in young and older adults: an fMRI study

Young and older adults assessed the approximate number of dots in collections including between 20 and 50 dots, with two strategies. The benchmark strategy is based on retrieving memory representations of quantities after visually scanning stimulus. The anchoring strategy involves both enumeration and estimation processes. Brain activations and performance were analyzed as a function of strategies, size of collections and age. Executing the benchmark strategy produced faster performance. It was associated with increased activity of a bilateral parieto/occipital and insular cortical network, including the postcentral gyrus, the cuneus, the middle occipital gyrus, and the insula. In addition to these bilateral activations, the benchmark strategy activated right prefrontal area. The anchoring strategy activated right superior parietal lobule, bilateral subcortical structures (putamen), and left dorso-lateral prefrontal cortex. The effects of aging on these cortical networks depended on strategies. These results suggest dissociation between two numerosity estimation strategies underlying different cognitive estimation processes and help to clarify age differences in numerosity estimation.

Neural representations of social status hierarchy in human inferior parietal cortex

Mental representations of social status hierarchy share properties with that of numbers. Previous neuroimaging studies have shown that the neural representation of numerical magnitude lies within a network of regions within inferior parietal cortex. However the neural basis of social status hierarchy remains unknown. Using fMRI, we studied subjects while they compared social status magnitude of people, objects and symbols, as well as numerical magnitude. Both social status and number comparisons recruited bilateral intraparietal sulci. We also observed a semantic distance effect whereby neural activity within bilateral intraparietal sulci increased for semantically close relative to far numerical and social status comparisons. These results demonstrate that social status and number comparisons recruit distinct and overlapping neuronal representations within human inferior parietal cortex.

Older and younger adults' strategies in approximate quantification

In two experiments, participants were asked to provide a quick and rough estimate of the number of items in collections of 4-79 items. In Experiment 1 verbal strategy reports and performance on each item were collected, and in Experiment 2 performance and eye movements were collected, while young and older participants were tested in strategy-instructed conditions. Results showed that: (a) participants used six different estimation strategies, (b) overall, young and older participants used the same set of strategies, but varied in how often they used each strategy, (c) older adults' strategy repertoire was smaller than young adults' (i.e., inter-individual differences in strategy repertoire), (d) strategy use, participants' performance, and eye movements varied as a function of numerosities and configurations of items, (e) in both the age groups, each strategy was associated with distinctive performance measures and eye movement patterns. These findings show that different processes are available for approximate quantification in both young and older adults and that aging is associated with strategic variations.

Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction

Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this task successfully with all the signatures of adults' nonsymbolic number representations: accuracy modulated by the ratio of the sum and the comparison quantity, equal performance for within- and cross-modality tasks and for addition and comparison tasks, and performance superior to that of a matched subtraction task. The findings provide clear evidence for nonsymbolic numerical operations on abstract numerical quantities in children who have not yet been taught formal arithmetic.

Verbal numerosity estimation deficit in the context of spared semantic representation of numbers: a neuropsychological study of a patient with frontal lesions

Patients with frontal lobe damage have been shown to produce implausible answers in cognitive estimation, a task requiring approximate answers to quantity-related questions of general semantic knowledge. We investigated a patient with frontal lobe damage who presented executive deficits and difficulties in cognitive estimation. The patient also showed difficulties in verbal numerosity estimation (approximately evaluating the quantity of visually presented sets of items), as he produced extreme answers well outside healthy participants' range of answers. A series of tasks evidenced intact number processing and well preserved semantic representation of numbers. Detailed investigation of estimation processes suggested a deficit at the level of translation from an intact semantic representation of numbers to output, whether verbal or non-symbolic. This case study allows disentangling different processes involved in estimation and contributes to a better understanding of the cognitive estimation deficits frequently reported for patients with frontal lesions.

The multiple dimensions of sustained attention

Sustained counting (or temporal numerosity judgements) has been one of the key means of investigating anterior attentional processes. Forty-three patients with localised lesions to the frontal lobes were assessed on two tests of the ability to count the number (8-22) of stimuli presented at either a slow (roughly one per 3 sec) or fast (roughly three per sec) rate. Patients with lesions to the Superior Medial (SM) region (particularly Brodmann areas 24, 32, and 9) were impaired both in the Slow condition and also in the Fast condition, where they underestimated the number of stimuli. Patients with Right Lateral (RL) lesions (8, 45, and 46) also had difficulties in the Fast condition, especially when the number of targets was greater than 15. The results are considered from the perspectives of alternative positions on anterior attentional processes developed by Posner and Petersen (1990) and by Stuss et al. (1995). The most plausible interpretation is in terms of energising processes which involve the SM frontal cortex and monitoring processes which involve the RL frontal cortex.

Why frequencies are natural

Research in mathematical cognition has shown that rates, and other interpretations of x/y, are hard to learn and understand. On the other hand, there is extensive evidence that the brain is endowed with a specialized mechanism for representing and manipulating the numerosities of sets – that is, frequencies. Hence, base-rates are neglected precisely because they are rates, whereas frequencies are indeed natural.

Does the parietal cortex distinguish between "10," "ten," and ten dots?

It is well established that the intraparietal sulcus (IPS) plays an important role in the processing and representation of numerical magnitude. Two recent studies by Piazza et al. and Cohen Kadosh et al. published in this issue of Neuron used fMRI adaptation to explore the extent to which parietal number processing is dependent upon or independent of a numbers' surface format. Their results, while slightly different, converge to suggest that the answer may be neither, but rather that it depends on the hemisphere.

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

Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in various number-processing tasks, whether numbers were conveyed by symbolic numerals (digits, number words) or by nonsymbolic displays (dot patterns). This suggests an abstract coding of numerical magnitude. Here, we critically tested this hypothesis using fMRI adaptation to demonstrate notation-independent coding of numerical quantity in the hIPS. Once subjects were adapted either to dot patterns or to Arabic digits, activation in the hIPS and in frontal regions recovered in a distance-dependent fashion whenever a new number was presented, irrespective of notation changes. This remained unchanged when analyzing the hIPS peaks from an independent localizer scan of mental calculation. These results suggest an abstract coding of approximate number common to dots, digits, and number words. They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities.