The number sense in the human brain

Humans and other species are endowed with perceptual mechanisms dedicated to estimating approximate quantity, an ability that has been defined as a sense of number. Converging evidence gathered from neurophysiological, behavioural and imaging studies, support the idea that this number sense has a truly abstract nature, being capable of encoding the numerosity of any set of discrete elements, displayed simultaneously or sequentially, and across different sensory modalities (Nieder et al., 2006; Piazza et al., 2006; Burr & Ross, 2008). It has been shown that numerosity, like most other primary visual attributes, is highly susceptible to adaptation: visually inspecting for a few seconds a large number of items, simultaneously presented, results in the perceived numerosity of a subsequent ensemble to be strongly underestimated, and vice-versa after adaptation to low numbers (Burr & Ross, 2008). Given that processing numerical information is also fundamental for the motor system to program sequences of self- movement, a further level of generalization of the number sense would be the possibility that a shared numerical representation exists between action and perception – that is, according to this view, the number sense would be generalized across presentation formats, sensory modalities, and perceptual and motor domains. In this work, we investigate numerosity perception within this theoretical framework. The first study was designed to investigate the perception of numerosity for stimuli presented sequentially by using an adaptation paradigm. This study tested whether, and to what extent, adaptation to a high or low number of events distorts the perceived numerosity of a subsequent sequence of visual events presented in the adapted location. In line with the typical dynamics of adaptation aftereffects, adapting to few events caused an overestimation of the perceived numerosity of the test stimuli, whilst adaptation to high-numerosity yielded a robustly underestimation. We further showed that adaptation effects transcend the sensory modality and presentation format: adapting to sequences of tones affected the perceived numerosity of a subsequently presented series of flashes (and vice versa), and adapting to sequences of flashes affected the perceived numerosity of spatial arrays of items. Similar results were obtained with tactile stimuli. Moreover, adaptation occurred only when test and adaptor positions were presented at the same location in spatiotopic (external world) coordinates, as demonstrated by introducing a saccadic eye movement between the offset of the adapting stimuli and the onset of the test stimuli (Arrighi et al., 2014). In the second part of this work, we present a subsequent work examining the possibility that the perceptual and the motor system might share a common numerical representation by using again the psychophysical technique of adaptation. In different sessions, we asked the subjects to produce either a fast (high number) or slow (low number) tapping routine. At the end of this adaptation phase subjects had to estimate the number of pulses presented sequentially, or of a cloud of dots simultaneously presented either on the same side where the motor actions were performed or on the opposite side. We found that motor adaptation strongly affected numerosity estimation of the test stimuli only when they were presented on the congruent side, with no effect when the visual stimuli were displayed on the neutral, not adapted, location. Moreover, to verify the robustness of the spatial selectivity, we repeated the experiment with a new subject pool, changing the tapping hand and location. Again, the spatial selectivity of the adaptation resulted to be in external – not hand-based – coordinates (Anobile, Arrighi et al., 2016). In the third part of this work we present another work where we evaluated the possibility that vision could drive the development of an external coordinate system for perceived numbers. In this study, congenitally blind (CB) and sighted controls (SC) were asked to evaluate the numerosity of sounds after performing either slow or fast motor adaptation (tapping), with the dominant hand, either in an uncrossed or in a crossed posture. Robust adaptation effects were observed in both groups of participants: an underestimation of the numerosity presented was observed after the execution of fast movements and an overestimation of the numerosity was observed after the execution of slow movements, in the crossed as well as in the uncrossed posture. Taken together, these results expand previous findings showing that adaptation to self-produced actions distorts perceived numerosity of sounds. Moreover, we demonstrate that visual experience is not necessary for the development of an external coordinate system for the shared numerical representation across action and perception. Finally, in the last part of this work, we examine the possibility of a common neural mechanism for different magnitude dimensions. Indeed, it has been recently proposed that space, time, and number might share a common representation in the human brain. For example, adaptation to visual motion affects both perceived position and duration of subsequent stimuli presented in the adapted location, suggesting that adaptation to visual motion distorts spatial maps as well as time processing (Johston et al. 2006, Burr et al., 2007; Fornaciai et al., 2016). In this study, we tested whether motion adaptation also affects perceived numerosity. Adaptation to fast translational motion yielded a significant reduction in the apparent numerosity of the adapted stimulus (of about 25%), while adaptation to slow translational or circular motion (both 20Hz and 5Hz) yielded a weaker but still significant compression of perceived numerosity. Our results generally support the idea of a common system for processing of space, time and number. However, as changes in perceived numerosity co-varied with both adapting motion profiles and speed, our evidence suggest a complex and asymmetric interactions between the representations of space, time and number in the brain. Taken together, the results obtained across these studies point to the existence of a generalized mechanism for numerical representation in the brain that is amodal, independent of the presentation format, shared between the perceptual and the motor systems, and based on external coordinate system.