How Evolution Constrains Human Numerical Concepts

Spatial associations of number and pitch in human newborns

Humans use space to think, reason about, externally represent, and even talk about many dimensions (e.g., time, pitch height). One dimension that appears to exploit spatial resources is the mental representation of the numerosity of a set in the form of a mental number line. Although the horizontal number-space mapping is present from birth (small-left vs. large-right), it is unknown whether it extends to other spatial axes from birth or whether it is later acquired through development/experience. Moreover, newborns map changes in pitch height onto a vertical axis (low pitch-bottom vs. high pitch-top), but it is an open question whether it extends to other spatial axes. We presented newborns (N = 64 total, n = 16 per experiment, 0-4 days) with an auditory increase/decrease in magnitude along with a visual figure on a vertically oriented screen (bottom vs. top, change in number: Experiments 1 and 2; change in pitch: Experiment 3) or on a horizontally oriented screen (left vs. right, change in pitch: Experiment 4). Newborns associated changes in magnitude with a vertical axis only when experiencing an increase in magnitude (increase/up); however, the possibility that visuospatial biases could account for this asymmetric pattern are discussed. Newborns did not map changes in pitch horizontally (Experiment 4), in line with previous work showing that the horizontal mapping of number at birth does not generalize to other dimensions. These findings suggest that the flexible use of different spatial axes to map magnitude is not functional at birth and that the horizontal mapping of number might be privileged.

What makes different number-space mappings interact?

Models of numerical cognition consider a visuo-spatial representation to be at the core of numerical processing, the 'mental number line'. Two main interference effects between number and space have been described: the SNARC effect reflects a small number/left side and large number/right side association (number-location mapping); the size-congruity effect (SCE) reflects a small number/small size and large number/large size association (number-size mapping). Critically, a thorough investigation on the representational source for these two number-space mappings is lacking, leaving open the question of whether the same representation underlies both phenomena. Here, we build on a recent study (Viarouge and de Hevia in Front Hum Neurosci 15:750964, 2021) in order to address this question in three experiments, by systematically manipulating the presence of the two conditions that might elicit an interaction between SNARC and SCE: (i) an implicit task whereby numerical and spatial information are task-irrelevant, (ii) a design in which the number-space congruency relative to both mappings vary at the same level -either both within or between blocks. Experiment 1 replicated the interaction between the two mappings when both factors were present. Experiments 2 and 3 dissociated the two factors by varying the two mappings at the same level but using an explicit comparison task (Experiment 2), or by using an implicit task but with mappings varying at different levels (Experiment 3). We found that both factors, either in combination or used in isolation, drive the interaction between the two number-space mappings. These findings are discussed in terms of the weight given to each mapping, suggesting that a single representation encompassing both number-space mappings is therefore activated whenever both mappings are given equal weight through task requirements.

Intuitive mapping between nonsymbolic quantity and observed action across development

Adults' concurrent processing of numerical and action information yields bidirectional interference effects consistent with a cognitive link between these two systems of representation. This link is in place early in life: infants create expectations of congruency across numerical and action-related stimuli (i.e., a small [large] hand aperture associated with a smaller [larger] numerosity). Although these studies point to a developmental continuity of this mapping, little is known about the later development and thus how experience shapes such relationships. We explored how number-action intuitions develop across early and later childhood using the same methodology as in adults. We asked 3-, 6-, and 8-year-old children, as well as adults, to relate the magnitude of an observed action (a static hand shape, open vs. closed, in Experiment 1; a dynamic hand movement, opening vs. closing, in Experiment 2) to either a small or large nonsymbolic quantity (numerosity in Experiment 1 and numerosity and/or object size in Experiment 2). From 6 years of age, children started performing in a systematic congruent way in some conditions, but only 8-year-olds (added in Experiment 2) and adults performed reliably above chance in this task. We provide initial evidence that early intuitions guiding infants' mapping between magnitude across nonsymbolic number and observed action are used in an explicit way only from late childhood, with a mapping between action and size possibly being the most intuitive. An initial coarse mapping between number and action is likely modulated with extensive experience with grasping and related actions directed to both arrays and individual objects.

Spontaneous supra-modal encoding of number in the infant brain

The core knowledge hypothesis postulates that infants automatically analyze their environment along abstract dimensions, including numbers. According to this view, approximate numbers should be encoded quickly, pre-attentively, and in a supra-modal manner by the infant brain. Here, we directly tested this idea by submitting the neural responses of sleeping 3-month-old infants, measured with high-density electroencephalography (EEG), to decoders designed to disentangle numerical and non-numerical information. The results show the emergence, in approximately 400 ms, of a decodable number representation, independent of physical parameters, that separates auditory sequences of 4 vs. 12 tones and generalizes to visual arrays of 4 vs. 12 objects. Thus, the infant brain contains a number code that transcends sensory modality, sequential or simultaneous presentation, and arousal state.

The evolution of quantitative sensitivity

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability.

This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.

Can a Single Representational Object Account for Different Number-Space Mappings?

Numbers are mapped onto space from birth on, as evidenced by a variety of interactions between the processing of numerical and spatial information. In particular, larger numbers are associated to larger spatial extents (number/spatial extent mapping) and to rightward spatial locations (number/location mapping), and smaller numbers are associated to smaller spatial extents and leftward spatial locations. These two main types of number/space mappings (number/spatial extent and number/location mappings) are usually assumed to reflect the fact that numbers are represented on an internal continuum: the mental number line. However, to date there is very little evidence that these two mappings actually reflect a single representational object. Across two experiments in adults, we investigated the interaction between number/location and number/spatial extent congruency effects, both when numbers were presented in a non-symbolic and in a symbolic format. We observed a significant interaction between the two mappings, but only in the context of an implicit numerical task. The results were unaffected by the format of presentation of numbers. We conclude that the number/location and the number/spatial extent mappings can stem from the activation of a single representational object, but only in specific experimental contexts.

Individually distinctive features facilitate numerical discrimination of sets of objects in domestic chicks

Day-old domestic chicks approach the larger of two groups of identical objects, but in a 3 vs 4 comparison, their performance is random. Here we investigated whether adding individually distinctive features to each object would facilitate such discrimination. Chicks reared with 7 objects were presented with the operation 1 + 1 + 1 vs 1 + 1 + 1 + 1. When objects were all identical, chicks performed randomly, as expected (Experiment 1). In the remaining experiments, objects differed from one another due to additional features. Chicks succeeded when those features were differently oriented segments (Experiment 2) but failed when the features were arranged to depict individually different face-like displays (Experiment 3). Discrimination was restored if the face-like stimuli were presented upside-down, disrupting global processing (Experiment 4). Our results support the claim that numerical discrimination in 3 vs 4 comparison benefits from the presence of distinctive features that enhance object individuation due to individual processing. Interestingly, when the distinctive features are arranged into upright face-like displays, the process is susceptible to global over local interference due to configural processing. This study was aimed at assessing whether individual object processing affects numerical discrimination. We hypothesise that in humans similar strategies aimed at improving performance at the non-symbolic level may have positive effects on symbolic mathematical abilities.

Interactions between language, thought, and perception: Cognitive and neural perspectives

ABSTRACT The role that language plays in shaping non-linguistic cognitive and perceptual systems has been the subject of much theoretical and experimental attention over the past half-century. Understanding how language interacts with non-linguistic systems can provide insight into broader constraints on cognitive and brain organization. The papers that form this volume investigate various ways in which linguistic structure can interact with and influence how speakers think about and perceive the world, and the related issue of the constraints that in turn shape linguistic representations. These theoretical and empirical contributions support deeper understanding of the interactions between language, thought, and perception, and motivate new approaches for developing directional predictions at both the neural and cognitive levels.