Numbers can be used most flexibly to quantify, rank and identify. 'Cardinal' number refers to quantitative number assignments assessing set size (numerosity), whereas 'ordinal' number applies to numerical rank, which concerns serial order. Finally, nominal number identifies objects.
The development of a full-blown, systematic number concept is only possible through language. However, animals and humans are nonetheless able to non-verbally grasp the cardinality of objects in order to judge numerical quantity, as well as serial order to allow them to assess numerical rank. So, numerical competence did not emerge de novo in linguistic humans, but built up on biological precursor systems.
Behavioural studies have shown that non-linguistic animals have the capacity to assess numerical quantity and rank. Animals have been trained to discriminate numerosities in a controlled laboratory setting, and animals in the wild have been shown to spontaneously use numerical information to allow them to make informed choices in their natural environment. List learning, which is the ability to encode and then retrieve an arbitrary list of items in their correct order, opened a window for studying how the ordinal rank of objects is learned and stored by animals. Moreover, pre-verbal human infants of several months of age already have the capacity to represent cardinality. Finally, some indigenous human cultures that lack number words or have a restricted concept of verbal counting can only estimate the number of items in a set by means of a non-verbal quantification system.
Single-cell recordings in monkeys and functional imaging studies in humans have helped to identify the neural basis of numerical competence. Quantity information is represented in the posterior parietal cortex in close association with the prefrontal cortex. The response properties of numerosity-selective cortical cells can explain basic psychophysical phenomena, such as the numerical distance effect and the numerical size effect. In humans, the intraparietal sulcus of the parietal lobe is specifically activated by non-verbal and verbal quantity information, independently of sensory modality, symbolic notation or cognitive status.
In monkeys, numerical rank, irrespective of the sensory properties of the objects involved, is encoded by neurons in the lateral prefrontal cortex. Neurons that encode the ordinal position of task-related hand or eye movements have been found in a variety of motor-related cortical areas in trained monkeys. In addition, in functional imaging studies in humans, the prefrontal and parietal cortices have also been found to be more strongly activated for order information.
Together, neural data on numerosity and serial order indicate that numerical quantity and rank order information are likely to share the same neural system, with the prefrontal cortex and the intra-parietal sulcus as key structures.
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.
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I thank I. Diester, O. Tudusciuc and K. Seymour for valuable comments on the manuscript. I. Diester provided figure 3a. My work is supported by a research group grant of the German Research Foundation and a career development award of the Human Frontier Science Program. Dedicated to Philipp.
The author declares no competing financial interests.
- HABITUATION–DISHABITUATION PROTOCOL
When repeatedly confronted with displays of a given number of visual objects (for example, two), infants will habituate to this numerosity and their looking time to the displays will decrease, but they will regain interest (dishabituate) if they are then presented with a display containing a different numerosity (for example, three).
Calculation deficits that are a result of developmental defects in the brain.
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Nieder, A. Counting on neurons: the neurobiology of numerical competence. Nat Rev Neurosci 6, 177–190 (2005). https://doi.org/10.1038/nrn1626
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