A Sensorimotor Numerosity System
Authors: Giovanni Anobile, Roberto Arrighi, Elisa Castaldi, David C. Burr
Journal: Trends in Cognitive Sciences (2020)

Behavioral studies show that humans and other animals can estimate the numerosity of both external stimuli and self-produced actions.Recent psychophysical studies using motor-adaptation techniques have characterized the link between action and magnitude perception, advancing the concept of a sensorimotor system encoding both external stimuli and internally generated actions.The sensorimotor numerosity system might reside in the parietal cortex. Incoming sensory input provides information for the planning and execution of actions, which yield motor outcomes that are themselves sensory inputs. One dimension where action and perception strongly interact is numerosity perception. Many non-human animals can estimate approximately the number of external elements as well as their own actions, and neurons have been identified that respond to both. Recent psychophysical adaptation studies on humans also provide evidence for neural mechanisms responding to both the number of externally generated events and self-produced actions. Here we advance the idea that these strong connections may arise from dedicated sensorimotor mechanisms in the brain, part of a more generalized system interfacing action with the processing of other quantitative magnitudes such as space and time. Incoming sensory input provides information for the planning and execution of actions, which yield motor outcomes that are themselves sensory inputs. One dimension where action and perception strongly interact is numerosity perception. Many non-human animals can estimate approximately the number of external elements as well as their own actions, and neurons have been identified that respond to both. Recent psychophysical adaptation studies on humans also provide evidence for neural mechanisms responding to both the number of externally generated events and self-produced actions. Here we advance the idea that these strong connections may arise from dedicated sensorimotor mechanisms in the brain, part of a more generalized system interfacing action with the processing of other quantitative magnitudes such as space and time. Early physiological studies suggested that the cerebral cortex is organized in many areas, each functionally specialized to analyze different features of the perceptual environment [1.Zeki S. A Vision of the Brain. Blackwell Scientific, 1993Google Scholar,2.Zeki S.M. Functional specialisation in the visual cortex of the rhesus monkey.Nature. 1978; 274: 423-428Crossref PubMed Scopus (577) Google Scholar]. Recent work, however, is beginning to show very strong interactions between different perceptual features, pointing to shared associative mechanisms. 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This theory has spawned multiple studies investigating how the perception of space, time, and number relies on shared mechanisms, with less attention dedicated to how perceptual information combines with action programming and execution. Here we propose that, for the perception of number, or numerosity (see Glossary), there exists a common neural system subserving both action and perception: a sensorimotor numerosity system, tuned to numerosity signals from both perception and action planning and execution. This proposal is supported by a range of studies suggesting that mechanisms processing the numerosity of externally generated events (regardless of sensory modality or presentation format) may also process internally generated events, such as goal-directed motor routines. We also review evidence suggesting that a sensorimotor system of this type may process quantitative information of non-numerical dimensions such as space and time. The number of items is represented in humans by two distinct processes: a cultural and language-dependent system that encodes precisely the cardinality of elements; and a more primitive system shared with a variety of non-human species termed the approximate number system (ANS), which encodes quantity (or numerosity) in an approximate, non-symbolic manner [5.Dehaene S. The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition. Oxford University Press, 2011Google Scholar,6.Burr D.C. et al.Psychophysical evidence for the number sense.Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci. 2017; 373: 20170045Crossref PubMed Scopus (39) Google Scholar]. Numerosity perception differs from both symbolic number representation (digits) and serial counting, in that it is rapid, parallel, and approximate. Numerosity estimation errors scale proportionally to physical numerosity, following Weber's law, at least over a limited range [7.Ross J. Visual discrimination of number without counting.Perception. 2003; 32: 867-870Crossref PubMed Scopus (53) Google Scholar,8.Anobile G. et al.Separate mechanisms for perception of numerosity and density.Psychol. Sci. 2014; 25: 265-270Crossref PubMed Scopus (99) Google Scholar]. This opinion deals almost exclusively with the notion of numerosity, so the proposed functional and anatomical mechanisms may be distinct from those dedicated to processing exact quantities. Humans and animals can estimate the numerosity not only of external events, but also of self-generated actions. For example, mice learn to press a lever a defined number of times for a reward, with average responses and variability increasing proportionally to the target number of repetitions (scalar variability) [9.Cavdaroglu B. Balci F. Mice can count and optimize count-based decisions.Psychon. Bull. Rev. 2016; 23: 871-876Crossref PubMed Scopus (9) Google Scholar]. 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Monkeys were trained to perform an arm movement (e.g., push) five times, then to switch to another movement (e.g., turn) for another five times and then back to the initial movement. Around a third of the cells in sensorimotor area 5 were selectively tuned to a specific repetition of the motor routine, shown by the normalized activity of the number-action cells in Figure 1C. Furthermore, transient pharmacological inactivation caused numerical errors in repetition of actions (while not producing motor deficits), demonstrating a causal link between the activity of these neurons and action numerosity [26.Sawamura H. et al.Deficits in action selection based on numerical information after inactivation of the posterior parietal cortex in monkeys.J. Neurophysiol. 2010; 104: 902-910Crossref PubMed Scopus (29) Google Scholar]. Given the low numerosities involved (around 5), monkeys may have engaged in counting rather than estimation, but the study nevertheless demonstrates a clear link between number and action. There is also evidence for numerosity tuning of single-cell activity from the medial temporal lobe (MTL) of human neurosurgical patients performing calculation tasks on symbolic and non-symbolic stimuli [27.Kutter E.F. et al.Single neurons in the human brain encode numbers.Neuron. 2018; 100: 753-761.e4Abstract Full Text Full Text PDF PubMed Scopus (30) Google Scholar]. The first operand and the subsequent delay period elicited clear responses from the hippocampus, parahippocampal cortex, entorhinal cortex, and amygdala for both non-symbolic (Figure 1D) and symbolic numbers. Most number-selective cells were found in the parahippocampal cortex, which is highly interconnected with frontal and parietal areas. 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A network of topographic numerosity maps in human association cortex.Nat. Hum. Behav. 2017; 1: 0036Crossref Scopus (40) Google Scholar] have revealed topographically organized maps (NCP1–3) in partial overlap with these regions, which are selective to non-symbolic numerosities. Like the macaque VIP, area NCP1 is located posterior to a region of visual tactile convergence (Figure 2B [33.Harvey B.M. et al.Comparing parietal quantity-processing mechanisms between humans and macaques.Trends Cogn. Sci. 2017; 21: 779-793Abstract Full Text Full Text PDF PubMed Scopus (14) Google Scholar]). This region may correspond to area 5 [40.Gentile G. et al.Integration of visual and tactile signals from the hand in the human brain: an FMRI study.J. 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Interestingly, a recent study found that a nearby parietal area with another numerosity map (area NCP3) is recruited during numerical processing of observed actions [42.Sawamura H. et al.A parietal region processing numerosity of observed actions: an FMRI study.Eur. J. Neurosci. 2020; (Published online August 3, 2020. https://doi.org/10.1111/ejn.14930)Crossref PubMed Scopus (2) Google Scholar]. Other studies identified a multisensory homunculus along the posterior central sulcus (PoCS), posterior to the primary somatosensory cortex and extending into the inferior PoCs and anterior intraparietal sulcus. The hand representation is 'out of order' and located lateral and anterior to the region VIP+ [responsive to tactile stimulation of the face (Figure 2C); for a review see [43.Huang R.S. Sereno M.I. Multisensory and sensorimotor maps.Handb. Clin. Neurol. 2018; 151: 141-161Crossref PubMed Scopus (17) Google Scholar]). Upper and lower limbs are also represented intermingled in a more medial region in the superior parietal lobe. These areas have been implicated in the sensory and visuomotor control of actions such as reaching and grasping and defensive and feeding behaviors (Figure 2D). The proximity of areas supporting hand movements and numerosity representation may mediate the psychophysical interaction between hand tapping and numerosity, which we will discuss in some detail. Overall, given the role in sensorimotor integration and action guidance played by these areas, it is likely that they are implicated in the behavioral interactions between numerosity and action. Together with the prefrontal cortex, implicated in the maintenance of working memory of supramodal (visual, auditory, and tactile) numerosity information [44.Spitzer B. et al.Parametric alpha- and beta-band signatures of supramodal numerosity information in human working memory.J. 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Adaptation usually causes misperception of specific aspects of the stimulus, such as direction of motion, which become biased in the opposite direction to the adaptor: after observing for a few seconds the downward movement of a waterfall, shifting gaze to the adjacent region will cause it to appear to move upward [78.Addams R. An account of a peculiar optical phaenomenon seen after having looked at a moving body.Lond. Edinb. Philos. Mag. J. Sci. 1834; 5: 1Google Scholar]. This phenomenon is attributed to an imbalance in the relative activities of neurons tuned to vertical motion after sustained stimulation of those tuned to downward motion. The test stimulus will then tap a system that is functionally unbalanced, producing measurable illusory perceptual aftereffects. This technique can reveal neural populations sensitive to the tested feature (e.g., numerosity) and give information on how it is functionally organized, revealing selectivity to specific stimulus features such as motion direction, orientation, size, perceptual numerosity (Figure I), and many others [49.Thompson P. Burr D. Visual aftereffects.Curr. Biol. 2009; 19: R11-R14Abstract Full Text Full Text PDF PubMed Scopus (120) Google Scholar]. Adaptation is ubiquitous throughout all sensory systems, representing a form of short-term plasticity, probably serving as a tool to calibrate perception to their environment statistics [68.Solomon S.G. Kohn A. Moving sensory adaptation beyond suppressive effects in single neurons.Curr. Biol. 2014; 24: R1012-R1022Abstract Full Text Full Text PDF PubMed Scopus (111) Google Scholar,69.Barlow H.B. A theory about the functional role and synaptic mechanism of visual aftereffects.in: Blakemore C.B. Vision: Coding and Efficiency. 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Adaptation usually causes misperception of specific aspects of the stimulus, such as direction of motion, which become biased in the opposite direction to the adaptor: after observing for a few seconds the downward movement of a waterfall, shifting gaze to the adjacent region will cause it to appear to move upward [78.Addams R. An account of a peculiar optical phaenomenon seen after having looked at a moving body.Lond. Edinb. Philos. Mag. J. Sci. 1834; 5: 1Google Scholar]. This phenomenon is attributed to an imbalance in the relative activities of neurons tuned to vertical motion after sustained stimulation of those tuned to downward motion. The test stimulus will then tap a system that is functionally unbalanced, producing measurable illusory perceptual aftereffects. This technique can reveal neural populations sensitive to the tested feature (e.g., numerosity) and give information on how it is functionally organized, revealing selectivity to specific stimulus features such as motion direction, orientation, size, perceptual numerosity (Figure I), and many others [49.Thompson P. Burr D. Visual aftereffects.Curr. Biol. 2009; 19: R11-R14Abstract Full Text Full Text PDF PubMed Scopus (120) Google Scholar]. Adaptation is ubiquitous throughout all sensory systems, representing a form of short-term plasticity, probably serving as a tool to calibrate perception to their environment statistics [68.Solomon S.G. Kohn A. Moving sensory adaptation beyond suppressive effects in single neurons.Curr. Biol. 2014; 24: R1012-R1022Abstract Full Text Full Text PDF PubMed Scopus (111) Google Scholar,69.Barlow H.B. A theory about the functional role and synaptic mechanism of visual aftereffects.in: Blakemore C.B. Vision: Coding and Efficiency. 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