Number Forms in the Brain

Journal of Cognitive Neuroscience, 2005

In synesthesia, certain stimuli (“inducers”) may give rise to perceptual experience in additional modalities not normally associated with them (“concurrent”). For example, color-grapheme synesthetes automatically perceive achromatic numbers as colored (e.g., 7 is turquoise). Although synesthetes know when a given color matches the one evoked by a certain number, colors do not automatically give rise to any sort of number experience. The behavioral consequences of synesthesia have been documented using Stroop-like paradigms, usually using color judgments. Owing to the unidirectional nature of the synesthetic experience, little has been done to obtain performance measures that could indicate whether bidirectional cross-activation occurs in synesthesia. Here it is shown that colors do implicitly evoke numerical magnitudes in color-grapheme synesthetes, but not in nonsynesthetic participants. It is proposed that bidirectional co-activation of brain areas is responsible for the links bet...

Cortex, 2018

Over-learned semantic representations, such as numbers, are strongly associated with space in normal cognition, and in the phenomenon called number-space synaesthesia. In number-space synaesthesia, numbers are linked to spatial locations in an idiosyncratic way. Synaesthetes report numbers as belonging to a specific location, or feelings that a specific location is the right location for that number. What does really differentiate synaesthetes from non-synaesthetes with respect to their number-space representation? Here we present a number-space synaesthete, MkM, whose number-space representation dramatically differs from that of controls. We examined the impact of spatial distance with respect to MkM's mental number line, and numerical distance with respect to the conceptualized horizontal representation of numbers. In a behavioural experiment, MkM and controls performed number comparison tasks in which they reported either the larger numerical value (number task) or the larger stimulus (physical task) (Experiment 1). A spatial distance effect was found only for MkM. In a brain imaging experiment, MkM and controls compared a single presented digit with an internal reference (Experiment 2). Consistent with the behavioural results, spatial distance elicited significant brain activations only for MkM in different cortical sites including the left supramarginal gyrus. Numerical distance elicited significant brain activations only for controls in the left somatosensory cortex and in the right operculum. We propose that two types of representation are accessed in synaesthesia: one derived by the semantic coding of numbers across space (described by the mental number line), and an explicit spatial representation derived from the position of number within the synaesthetic association.

Frontiers in Psychology, 2013

Numerical synesthesia is more than just a symbolinduced phenomenon. Front. Psychol. 4:860.

Neuron, 2003

Johann-Wolfgang-Goethe University These processes range from nonspecific instrumental Frankfurt a.M. components such as attention, working memory, lan-Germany guage, and visuospatial processes to the specific operations mediating exact or approximate calculation. It is virtually impossible to construe control tasks that match Summary the precise demands imposed on instrumental cognitive processes but do not rely on numbers or magnitude The triple-code theory of numerical processing postuinformation. In terms of neural activity, these instrumenlates an abstract-semantic "number sense." Neurotal processes form a powerful confound, and accordpsychology points to intraparietal cortex as a potential ingly, recent work has confirmed that the cortical netsubstrate, but previous functional neuroimaging studworks activated by nonarithmetic operations performed ies did not dissociate the representation of numerical on numbers or even letters are comparably strong as magnitude from task-driven effects on intraparietal and barely distinguishable from those underlying true activation. In an event-related fMRI study, we pre-

Cognitive Neuropsychology, 2006

There is a universal and often unconscious tendency to mentally associate the number sequence with a spatial continuum (the mental number line). Here we study one individual who reports a strong and vivid sense of space when processing numbers. For him, the number sequence has a precise spatial form: a curvilinear right-to-left oriented line. We used various tasks to demonstrate that this numerical -spatial association is not a mere figment of his imagination, but a constrained experiential phenomenon consistent across sessions and automatically triggered by the visual presentation of numbers. We also show that this idiosyncratic representation can coexist with another implicit association, the SNARC effect (Spatial -Numerical Association of Response Codes, where small numbers are associated with the left side of space). This effect is present in individuals without explicit number forms and is not affected in the present subject in spite of his reversed subjective representation.

NeuroReport, 2005

Frontiers in Integrative Neuroscience, 2012

Humans and animals appear to share a similar representation of number as an analog magnitude on an internal, subjective scale. Neurological and neurophysiological data suggest that posterior parietal cortex (PPC) is a critical component of the circuits that form the basis of numerical abilities in humans. Patients with parietal lesions are impaired in their ability to access the deep meaning of numbers. Acalculiac patients with inferior parietal damage often have difficulty performing arithmetic (2 + 4?) or number bisection (what is between 3 and 5?) tasks, but are able to recite multiplication tables and read or write numerals. Functional imaging studies of neurologically intact humans performing subtraction, number comparison, and non-verbal magnitude comparison tasks show activity in areas within the intraparietal sulcus (IPS). Taken together, clinical cases and imaging studies support a critical role for parietal cortex in the mental manipulation of numerical quantities. Further, responses of single PPC neurons in non-human primates are sensitive to the numerosity of visual stimuli independent of low-level stimulus qualities. When monkeys are trained to make explicit judgments about the numerical value of such stimuli, PPC neurons encode their cardinal numerical value; without such training PPC neurons appear to encode numerical magnitude in an analog fashion. Here we suggest that the spatial and integrative properties of PPC neurons contribute to their critical role in numerical cognition.

Abstract In adult human brains, the horizontal segment of the intraparietal sulcus plays a large role in representing numeric magnitude. In children and non-human primates, however, frontal cortex may play a larger role. We hypothesized that there is a link between observed developmental changes in locus of representation (frontal to parietal) and type of representation used (logarithmic to linear). Participants were presented with number lines and asked to judge accuracy of linear, logarithmic, or log-linear placements.

Journal oc Cognitive Neuroscience, 2012

The visual recognition of letters dissociates from the recognition of numbers at both the behavioral and neural level. In this article, using fMRI, we investigate whether the visual recognition of numbers dissociates from letters, thereby establishing a double dissociation. In Experiment 1, participants viewed strings of consonants and Arabic numerals. We found that letters activated the left midfusiform and inferior temporal gyri more than numbers, replicating previous studies, whereas numbers activated a right lateral occipital area more than letters at the group level. Because the distinction between letters and numbers is culturally defined and relatively arbitrary, this double dissociation provides some of the strongest evidence to date that a neural dissociation can emerge as a result of experience. We then investigated a potential source of the observed neural dissociation. Specifically, we tested the hypothesis that lateralization of visual number recognition depends on lateralization of higher-order numerical processing. In Experiment 2, the same participants performed addition, subtraction, and counting on arrays of nonsymbolic stimuli varying in numerosity, which produced neural activity in and around the intraparietal sulcus, a region associated with higher-order numerical processing. We found that individual differences in the lateralization of number activity in visual cortex could be explained by individual differences in the lateralization of numerical processing in parietal cortex, suggesting a functional relationship between the two regions. Together, these results demonstrate a neural double dissociation between letter and number recognition and suggest that higher-level numerical processing in parietal cortex may influence the neural organization of number processing in visual cortex.

2016

Perception of number and space are tightly intertwined. It has been proposed that this is due to 'cortical recycling', where numerosity processing takes over circuits originally processing space. Do such 'recycled' circuits retain their original functionality? Here, we investigate interactions between numerosity and motion direction, two functions that both localize to parietal cortex. We describe a new phenomenon in which visual motion direction adapts nonsymbolic numerosity perception, giving rise to a repulsive aftereffect: motion to the left adapts small numbers, leading to overestimation of numerosity, while motion to the right adapts large numbers, resulting in underestimation. The reference frame of this effect is spatiotopic. Together with the tuning properties of the effect this suggests that motion direction-numerosity cross-adaptation may occur in a homolog of area LIP. 'Cortical recycling' thus expands but does not obliterate the functions originally performed by the recycled circuit, allowing for shared computations across domains.

Cortex, 2011

Cortex, 2009

E.M. Hubbard). a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o r t e x 0010-9452/$ -see front matter ª c o r t e x 4 5 ( 2 0 0 9 ) 1 2 0 0 -1 2 1 6 c o r t e x 4 5 ( 2 0 0 9 ) 1 2 0 0 -1 2 1 6

The Neuroscientist, 2012

Neuropsychologia, 2017

Nature Reviews Neuroscience, 2005

The history of mathematics is traversed by a deep connection between numbers and space. From the most elementary aspects of mathematics, such as the notion of measurement, all the way up to the concepts of the real number line, Cartesian coordinates, the complex plane and even the proof of Fermat's Last Theorem, metaphors by which numbers are made to correspond to spatial positions permeate mathematical thinking 1-3 . The evolution of these culturally-defined representations of numbers has been crucial to the development of mathematics. In this review, we discuss the neural mechanisms that might underpin these cultural achievements. We begin by reviewing recent behavioural and patient data that show that certain aspects of numerical understanding depend on spatial representations. We then turn to neuroimaging data in humans, which indicate that the deep connection between numbers and space might be mediated by the neural circuitry in the parietal lobe. Drawing on recent work in monkey physiology and neuroimaging studies that established tentative monkey-human homologies, we then present a refined hypothesis about the specific neural regions in the INTRAPARIETAL SULCUS (IPS) that might be involved in these numerical and spatial processes, including the LATERAL INTRAPARIETAL (LIP) and VENTRAL INTRAPARIETAL (VIP) regions.