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Neural Bases of Number Sense

Bilateral intraparietal sulcus is the major site of activation in neuroimaging studies of number processing: it is active in mental arithmetic, more in arithmetic than in number reading, more active in approximate than exact calculation, more active for subtraction than multiplication; it is active in number comparison with a larger activation in the right hemisphere.

Neuropsychological evidence shows that people with severe calculation impairments present largely preserved language and semantic functions. Patients may fail to compute operations as simple as 2+2 or 3-1, regardless of presentation modality. They may still be able to comprehend and produce numbers in all formats. Dissociation between number meaning and general semantic memory was showed: spared calculation and number comprehension abilities in patient with severe semantic deficits, including semantic dementia, that usually spare the

intraparietal region. Calculation impairments often co-occur with other deficits, forming Gerstmann's syndrome (agraphia, finger agnosia, left-right discrimination difficulties). Main lesional correlate is the IPS. The IPS is activated even when they merely detect a digit among colors and letters (Eger et al. 2003). The intraparietal region seems to be associated with an abstract, amodal representation of numbers inasmuch as it can be activated by numbers presented in various culturally learned symbolic notations such as Arabic numerals and spelled-out or spoken number words (Eger et al. 2003).

In an event-related fMRI study, we presented numbers, letters, and colors in the visual and auditory modality, asking subjects to respond to target items within each category. In the absence of explicit magnitude processing, numbers compared with letters and colors across modalities activated

abilateral region in the horizontal intraparietal sulcus. This stimulus-driven number-specific intraparietal response supports the idea of a supramodal number representation.

Further clarifying the role of the IPS in semantic number representations are neuroimaging studies that have relied on nonsymbolic presentations of number as sets of dots or as series of tones. Even passively looking at a set of dots suffices to encode its numerosity and adapt to it so that the IPS later shows a rebound functional magnetic resonance imaging (fMRI) response when the number is changed by a sufficient amount (Piazza et al. 2004). This fMRI adaptation method has also been used to demonstrate a convergence of symbolic and nonsymbolic presentations of numbers toward a common representation of quantity in the IPS and prefrontal cortex (PFC) (Piazza et al. 2007). fMRI and event-related potentials (ERPs) have shown that number-related parietal activations are already present in four-year-old children as they attend to

The numerosity of sets (Cantlon et al. 2006, Temple & Posner 1998). To visualize more directly the brain’s responses to number in infants, Izard et al. (2008) recorded event-related potentials from three-month-old infants while they were presented with a continuous stream of sets of objects. The right parietal cortex responded to numerical novelty, whereas the left occipito-temporal cortex responded to object novelty. Thus, the parietal mechanism of numerosity extraction seems to be already functional prior to symbolized education in humans. This supports the idea of a language-independent human quantification system whose precursors can also be tackled in nonhuman primates.

Are numbers special? Functional overlap during number comparison and letter comparison suggests that hIPS encodes abstract order information rather than numerical magnitude (Fias et al., 2007). Multivariate pattern analysis (MVPA) applied to the data of Fias et al. associates number comparison and letter comparison to

Distinct clusters of voxels in IPS (Zorzi et al., 2011). Decoding individual numerical stimuli in human intraparietal cortex during a delayed comparison task (Eger et al., 2009, Current Biology). In experiment 1 (A), dot numerosities (4–32) were successfully discriminated from an intraparietal ROI comprising the most activated voxels (across all stimuli vs baseline) in each subject. In experiment 2 (B), numerical magnitudes 2–8 were either presented in symbolic or nonsymbolic format. A classifier trained on dots was highly accurate on dots but at chance on digits. However, the digit-trained classifier (which had modest prediction accuracy) generalized to dots, suggesting that format specific and format-invariant components coexist. (C) When focusing with neurophysiologically motivated localizer scans on the subregions functionally equivalent to LIP and VIP, both regions were found to encode information on individual nonsymbolic numerosities (8–34 dots) (Eger et al., 2015,

Cerebral Cortex). The functional equivalent of area LIP showed a more pronounced effect of numerical distance, compatible with a coarser representation of numerosity.

Numerosity may emerge as high-order visual feature (summary statistics) in a deep neural network that simply "observes" images of objects sets (with variable numerosity) without any information about the number (training data is unlabelled). Stoianov and Zorzi (2012) = we show that visual numerosity emerges as a statistical property of images through unsupervised learning. We used deep networks, multilayer neural networks that contain top-down connections and learn to generate sensory data rather than to classify it. The deep network had one 'visible' layer encoding the sensory data and two hierarchically organized 'hidden' layers. Crucially, learning concerned only efficient coding of the sensory data (that is, maximizing the likelihood of reconstructing the input) and not number discrimination.

as information about object numerosity was not provided. Analyses of the network computations revealed that most of the first hidden layer (HL1) neurons were center-surround detectors that uniformly covered the image space. Also, the numerosity detectors in HL2 were spatially selective (Fig. 1f). They received strong input from HL1 neurons with spatially aligned receptive fields. They also received inhibition from a few HL1 neurons that encoded cumulative area, thereby providing a normalization signal. Thus, the numerosity detectors encoded local, size-invariant numerosity. The population activity of HL2 numerosity detectors was well predicted by a linear combination of the population activity of the two types of HL1 neuron. We emphasize that the response properties of the hidden neurons were not stipulated in any way but represent an emergent property of the image data obtained without supervision. A variety of number neurons emerge in the deepest layer, from number sensitive monotonic,summationcoding to number selective gaussian coding). Population coding supports numerosity comparison with the same behavioural signature of human data (Weber's law for numbers). The influence of visual cues on numerosity perception reveals the limit conditions (or impairments) of the normalization process that yields perceptual invariance. Learning in the model leads to increased number acuity. No a prori number knowledge seems necessary for developing number sense. General architectural and learning constraints let numerosity emerge as latent structure of our sensory environment. EMBODIED COGNITION Traditional cognitive science has typically claimed that cognition is computation and that minds are programmes that run on brain hardware. It believes in an insular nature of thought. Cognition is cut off from the world in the sense that cognitive processes operate only on symbolic deliverances from the sense organs. Because cognition begins and ends with inputs to and outputs fromThe nervous system, it has no need for interaction with the real world outside it. So, knowledge representations are abstracted away from specific sensory and motor experiences, leading to amodal concepts. Limitations of this abstract view of knowledge representation have become apparent, foremost among them the grounding problem (Harnad 1990): If all properties of a concept are in turn defined through other propositions in the knowledge network, then such definitions remain ultimately trapped within the network itself—they never link to the sensory-motor world that imports unambiguous meaning into the knowledge representation. As a result of this critique and several empirical observations, we now experience a swing of the theoretical pendulum back toward emphasizing the importance of sensory and motor experiences as inevitable parts of our knowledge. This ''embodied cognition'' approach has become a powerful framework for studying the acquisition, representation,

According to the embodied cognition perspective, it needs to elevate the importance of body in the explanation of various cognitive abilities. According to Lakoff and Johnson, almost all our concepts derive originally from the use of metaphorical reasoning. However, there must be some basic concepts that human beings can understand without relying on metaphorical reasoning. These basic concepts, Lakoff and Johnson hold, stem directly from the type of body human beings possess and the manner in which this type of body interacts with the environment. Among the basic concepts, Lakoff and Johnson argue, are spatial ones like up, down, front, back, in, out, near, and far. Human understanding of these concepts derives from facts about human bodies. These basic concepts structure the meanings of happy and sad: "I'm feeling up. You are in high spirits. I'm feeling down. I'm depressed". But, beings with bodies quite distinct from human bodies could

not acquire the human concepts and so their concept of happiness would differ from human beings' concept of happiness. We would have different concepts of happiness because we have different kinds of bodies. Similarly, R. Wilson has urged that the use of pencil and paper to aid in the solution of, say, multiplication problems, marks an actual extension of a cognitive system. The pencil and paper are integrated so essentially into the cognitive act that there is no principled reason to distinguish these external items from the rest of the cognitive system involved in solving the multiplication problem. Hauk et al. (2004) reported activation in hand, leg, and face motor cortex as healthy adults passively read verbs referring to tongue, finger, or foot movements, respectively. Tschentscher et al. (2012) reported spontaneous finger cortical activation in response to passive number viewing. Numbers are embodied concepts. Number meaning, its magnitude is conveyed by its position on the MNL. In

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