Andreas Nieder

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.

Counting on neurons: the neurobiology of numerical competence

Numbers are an integral part of our everyday life — we use them to quantify, rank and identify objects. The verbal number concept allows humans to develop superior mathematical and logic skills that define technologically advanced cultures. However, basic numerical competence is rooted in biological primitives that can be explored in animals, infants and human adults alike. We are now beginning to unravel its anatomical basis and neuronal mechanisms on many levels, down to its single neuron correlate. Neural representations of numerical information can engage extensive cerebral networks, but the posterior parietal cortex and the prefrontal cortex are the key structures in primates.

Temporal and Spatial Enumeration Processes in the Primate Parietal Cortex

Humans and animals can nonverbally enumerate visual items across time in a sequence or rapidly estimate the set size of spatial dot patterns at a single glance. We found that temporal and spatial enumeration processes engaged different populations of neurons in the intraparietal sulcus of behaving monkeys. Once the enumeration process was completed, however, another neuronal population represented the cardinality of a set irrespective of whether it had been cued in a spatial layout or across time. These data suggest distinct neural processing stages for different numerical formats, but also a final convergence of the segregated information to form most abstract quantity representations.

Semantic associations between signs and numerical categories in the prefrontal cortex.

The utilization of symbols such as words and numbers as mental tools endows humans with unrivalled cognitive flexibility. In the number domain, a fundamental first step for the acquisition of numerical symbols is the semantic association of signs with cardinalities. We explored the primitives of such a semantic mapping process by recording single-cell activity in the monkey prefrontal and parietal cortices, brain structures critically involved in numerical cognition. Monkeys were trained to associate visual shapes with varying numbers of items in a matching task. After this long-term learning process, we found that the responses of many prefrontal neurons to the visual shapes reflected the associated numerical value in a behaviorally relevant way. In contrast, such association neurons were rarely found in the parietal lobe. These findings suggest a cardinal role of the prefrontal cortex in establishing semantic associations between signs and abstract categories, a cognitive precursor that may ultimately give rise to symbolic thinking in linguistic humans.

A labeled-line code for small and large numerosities in the monkey prefrontal cortex.

How single neurons represent information about the magnitude of a stimulus remains controversial. Neurons encoding purely sensory magnitude typically show monotonic response functions (“summation coding”), and summation units are usually implemented in models of numerosity representation. In contrast, cells representing numerical quantity exhibit nonmonotonic tuning functions that peak at their preferred numerosity (“labeled-line code”), but the restricted range of tested quantities in these studies did not permit a definite answer. Here, we analyzed both behavioral and neuronal representations of a broad range of numerosities from 1 to 30 in the prefrontal cortex of monkeys. Numerosity-selective neurons showed a clear and behaviorally relevant labeled-line code for all numerosities. Moreover, both the behavioral and neuronal tuning functions obeyed the Weber–Fechner Law and were best represented on a nonlinearly compressed scale. Our single-cell study is in good agreement with functional imaging data reporting peaked tuning functions in humans, demonstrating neuronal precursors for human number competence in a nonhuman primate. Our findings also emphasize that the manner in which neurons encode and maintain magnitude information may depend on the precise task at hand as well as the type of magnitude to represent and memorize.

Neural correlates of categories and concepts

The ability to readily adapt to novel situations requires something beyond storing specific stimulus-response associations. Instead, many animals can detect basic characteristics of events and store them as generalized classes. Because these representations are abstracted beyond specific details of sensory inputs and motor outputs, they can be easily generalized and adapted to new circumstances. Explorations of neural mechanisms of sensory processing and motor output have progressed to the point where studies can begin to address the neural basis of abstract, categorical representations. Recent studies have revealed their neural correlates in various cortical areas of the non-human primate brain.

Analog Numerical Representations in Rhesus Monkeys: Evidence for Parallel Processing

Monkeys have been introduced as model organisms to study neural correlates of numerical competence, but many of the behavioral characteristics of numerical judgments remain speculative. Thus, we analyzed the behavioral performance of two rhesus monkeys judging the numerosities 1 to 7 during a delayed match-to-sample task. The monkeys showed similar discrimination performance irrespective of the exact physical appearance of the stimuli, confirming that performance was based on numerical information. Performance declined smoothly with larger numerosities, and reached discrimination threshold at numerosity 4. The nonverbal numerical representations in monkeys were based on analog magnitudes, object tracking process (subitizing) could not account for the findings because the continuum of small and large numbers shows a clear Weber fraction signature. The lack of additional scanning eye movements with increasing set sizes, together with indistinguishable neuronal response latencies for neurons with different preferred numerosities, argues for parallel encoding of numerical information. The slight but significant increase in reaction time with increasing numerosities can be explained by task difficulty and consequently time-consuming decision processes. The behavioral results are compared to single-cell recordings from the prefrontal cortex in the same subjects. Models for numerosity discrimination that may account for these results are discussed.

Supramodal numerosity selectivity of neurons in primate prefrontal and posterior parietal cortices

Numerosity, the number of elements in a set, is a most abstract quantitative category. As such, it is independent of the sensory modality of its elements, i.e., supramodal. Because neuronal numerosity selectivity had never been compared directly across different sensory modalities, it remained elusive if and where single neurons encode numerosity irrespective of the items’ modality. Here, monkeys were trained to discriminate both the number of auditory sounds and visual items within the same session. While the monkeys performed this task, the activity of neurons was recorded in the lateral prefrontal cortex and ventral intraparietal sulcus, structures critically involved in numerical cognition. Groups of neurons in both areas encoded either the number of auditory pulses, visual items, or both. The finding of neurons responding to numerosity irrespective of the sensory modality supports the idea of a nonverbal, supramodal neuronal code of numerical quantity in the primate brain.

Seeing more than meets the eye: processing of illusory contours in animals

Abstract. This review article illustrates that mammals, birds and insects are able to perceive illusory contours. Illusory contours lack a physical counterpart, but monkeys, cats, owls and bees perceive them as if they were real borders. In all of these species, a neural correlate for such perceptual completion phenomena has been described. The robustness of neuronal responses and the abundance of cells argue that such neurons might indeed represent a neural correlate for illusory contour perception. The internal state of an animal subject (i.e., alert and behaving) seems to be an important factor when correlating neural activity with perceptual phenomena. The fact that the neural network necessary for illusory contour perception has been found in relatively early visual brain areas in all tested animals suggests that bottom-up processing is largely sufficient to explain such perceptual abilities. However, recent findings in monkeys indicate that feedback loops within the visual system may provide additional modulation. The detection of illusory contours by independently evolved visual systems argues that processing of edges in the absence of contrast gradients reflects fundamental visual constraints and not just an artifact of visual processing.

Perception and neuronal coding of subjective contours in the owl

Robust form perception and underlying neuronal mechanisms require generalized representation of object boundaries, independent of how they are defined. One visual ability essential for form perception is reconstruction of contours absent from the retinal image. Here we show that barn owls perceive subjective contours defined by grating gaps and phase-shifted abutting gratings. Moreover, single-neuron recordings from visual forebrain (visual Wulst) of awake, behaving birds revealed a high proportion of neurons signaling such subjective contours, independent of local stimulus attributes. These data suggest that the visual Wulst is important in contour-based form perception and exhibits a functional complexity analogous to mammalian extrastriate cortex.