Humans possess an inborn ability to represent, discriminate, and manipulate numerical quantities, an ability that is shared with many other species (Cantlon, 2018). This ability is supported by the approximate number system (or ANS, Burr and Ross, 2008; Dehaene, 2009; Odic and Starr, 2018), which allows us to estimate (and mentally manipulate) the approximate numerosity of a set without using any symbolic knowledge (language or counting). The main signature of this cognitive system is that the variable determining a successful discrimination is the ratio between the two numerosities to compare, so that the larger the ratio between them the better the discrimination, a signature that also governs discrimination for other continuous, perceptual dimensions (Feigenson et al., 2004). This core, numerical cognitive system is thought to show continuity in development, and therefore to support the acquisition of formal math and symbolic numerical representations, with individual differences in numerical acuity predicting, and correlating with, math scores later on in life (Halberda et al., 2008; Starr et al., 2013). Another crucial aspect characterizing numerical representations is their spatial signature. In fact, a widely accepted view on numerical cognition considers numbers as distributions of activation along a spatially oriented mental number line (Restle, 1970; Dehaene, 1992).

Interactions between number and spatial representations have been extensively described in the literature, using a variety of methods: from visuo-spatial tasks, such as line bisection and reproduction tasks, where numbers impact spatial performance (Fischer, 2001; de Hevia et al., 2006, 2008; de Hevia and Spelke, 2009; Viarouge and de Hevia, 2013), to numerical tasks, such as parity judgment or magnitude comparison, where visuo-spatial variables modulate numerical judgments (Dehaene et al., 1993; Fias, 1996; Fischer et al., 2003; Bulf et al., 2014). This bidirectional interaction has been described across ages in humans, from infants who from birth spontaneously associate small numbers to small spatial extents and leftward spatial locations and large numbers to large spatial extents and rightward spatial locations (de Hevia and Spelke, 2010; de Hevia et al., 2014, 2017; Bulf et al., 2016; Di Giorgio et al., 2019), through childhood (Girelli et al., 2000; de Hevia and Spelke, 2009; Patro and Haman, 2012) and up to adulthood (Dehaene et al., 1993; Fischer et al., 2003), and even in non-human animals, such as chicks and chimpanzees, who have been shown to exhibit lateralized spatial associations of numerical quantities similar to humans (Adachi, 2014; Drucker and Brannon, 2014; Rugani et al., 2015).

In general terms, the interactions between numerical and spatial information can be described according to two types of number-space mappings (de Hevia, 2021). On the one hand, numbers can be mapped onto corresponding spatial extents, with larger numbers associated with larger spatial extents. This type of mapping is well exemplified in the Stroop paradigm, also known as the size congruity effect (SCE): when subjects have to compare numerical quantities (be it in a symbolic or non-symbolic format), the information of physical size interacts with the quantity judgment, so that incongruent combinations (e.g., a small quantity occupying a large space) yield worse performance than congruent combinations (e.g., a small quantity occupying a small space). This type of interaction between size and number has also been described in line bisection tasks (e.g., de Hevia et al., 2006; de Hevia and Spelke, 2009) as well as in reproduction tasks (e.g., de Hevia et al., 2008; Viarouge and de Hevia, 2013), providing further support to the idea that number is mapped onto a corresponding physical spatial extent.

On the other hand, numbers can be associated with different, lateralized spatial locations. This phenomenon is represented by the Spatial Numerical Association of Response Codes (SNARC) effect, by which small numbers are associated with the left and large numbers with the right side of space (Dehaene et al., 1993), obtaining an advantage in performance when the response side/or number location and the numerical magnitude are aligned according to a left-to-right oriented representation, with increasing numbers toward the right. This effect might be modulated by factors such as scanning habits (left-to-right vs. right-to-left writing/reading direction: Shaki et al., 2009), and contextual experience factors (Pitt and Casasanto, 2020).

Besides a few exceptions (de Hevia et al., 2006, 2008; Cipora et al., 2020; de Hevia, 2021), most authors usually assume that these two types of mappings (number-extent and number-location) reflect the same representational object, often appealing to the activation of a “mental number line” when interpreting the source of the interaction between numerical and spatial information. In fact, any type of behavioral interaction between numerical and spatial information in a given task is accounted for by the idea that humans might represent different numerosities along an internal spatial continuum: the mental number line.

However, some findings cast doubt on this generally accepted assumption. First, humans at birth show evidence of a dissociation between the number-spatial extent and the number-spatial location mappings. In particular, from birth and during the first year of life, infants spontaneously create mappings between number and spatial extent that can be generalized to the dimension of time (de Hevia and Spelke, 2010; Srinivasan and Carey, 2010; de Hevia et al., 2014). In some conditions, newborns and infants are also able to create mappings between number and brightness (de Hevia and Spelke, 2013; Bonn et al., 2019) and brightness and loudness (Lewkowicz and Turkewitz, 1980), supporting the view that number-spatial extent mapping is not specific to numerical information and extends to other quantitative dimensions. However, while at birth and during infancy humans associate lateralized spatial locations (left vs. right) to different numerosities (small vs. large, respectively), this number-spatial location mapping does not generalize to dimensions other than number, like size and brightness (Bulf et al., 2016; de Hevia et al., 2017), supporting the view that these two number-space mappings reflect distinct cognitive phenomena, at least early in life.

Second, a subcomponent of the number-spatial position mapping, which reflects the spontaneous tendency to mentally organize ordered information along a spatially oriented axis, is extended to any ordered dimension even in infancy (Bulf et al., 2017; Bulf et al., 2022). This type of number-spatial location mapping differs from the lateralized one (i.e., left-small/right-large) in that while the first one is related to the ordinality of the information (i.e., first, second, third…), the latter one, as it is also the case for the number-spatial extent mapping, is tied to the information of magnitude (i.e., smaller vs. larger). The fact that numbers can reflect these two properties at the same time, ordinality and cardinality, partially explains why authors often consider that any numerical-spatial effect emanates from a single representational object. However, analogous effects for non-numerical information, such as a SNARC-like effect for items in a grocery list (Previtali et al., 2010), are hardly accounted for by invoking a mental number line.

Finally, the question of an absence or not of a dependency between the number-spatial extent and the number-spatial location mappings has not received, to our knowledge, explicit attention by researchers. However, in one experiment from a larger study investigating the automaticity of the activation of numerical magnitude, Fitousi et al. (2009) observed that the SNARC effect was independent of the SCE in a task where participants had to judge the physical size of Arabic digits, again going against the idea of both number-space mappings reflecting a single construct in adulthood.

The present study is aimed at further investigating the interaction between the number-spatial extent and the number-spatial location interactions within a single experimental session. If both mappings reflect the same psychological construct, i.e., the same representational object (e.g., large number = large size = right side of space), they should interact with each other. As a consequence, the congruency effect related to one mapping will be modulated by the congruency relative to the other mapping. For instance, if the number/location (resp. number/spatial extent) mapping is congruent, then there will be a number/spatial extent (resp. number/location) mapping, so that congruent trials will lead to higher performance relative to incongruent trials. For number/location (resp. number/spatial extent) incongruent mappings, no difference in performance should be observed between number/spatial extent (resp. number/location) congruent and incongruent trials. However, if both mappings reflect distinct representational objects, the congruency relative to one mapping should not impact the congruency effect related to the other mapping. If we assume that both congruency effects are unaffected by each other, this should in turn, lead to an overall additivity pattern, whereby the highest performance is observed in trials showing a congruency for both mappings, and the lowest performance is observed in trials showing an incongruency for both mappings (Figure 1).

It is possible that the interaction between the two mappings depends on the format of presentation of numbers. According to the infant literature mentioned above, we hypothesize distinct mappings with non-symbolic representations of numbers. However, with education, digits could be mapped onto multiple spatial dimensions (extent and location) in a more holistic manner, leading to stronger interactions between both mappings when processing symbolic numbers.

To test these predictions, we designed a numerical judgment task containing both number-extent and number-location congruent and incongruent trials. In order to directly assess the role of the format of presentation, each participant performed both a non-symbolic and a symbolic version of the task.

In this study we aimed at directly investigating the question of whether there is an interaction between two number-space mappings, i.e., the number/spatial extent and the number/spatial location mappings. We reported that, when using a numerical magnitude judgment task, the two mappings did not interact: the difference in performance between congruent and incongruent trials relative to one mapping was the same for congruent and incongruent trials relative to the other mapping (in line with the prediction Figure 1A). However, in the context of an implicit task, i.e., a color judgment task, using the same stimuli, the two mappings interacted, with stronger congruency effect relative to one mapping when the trials were congruent relative to the other mapping (in line with the prediction Figure 1B).

Altogether, our results suggest that both the number/extent and the number/location mappings can tap onto a shared representational object, but that its activation critically depends on the experimental context, and can manifest itself in different ways. Several factors could be at play. First, the reliance on a shared representational object for both mappings could depend on whether magnitude is implicitly or explicitly activated by the task. Both in Fitousi et al. (2009) and in the current study, using a task whereby magnitude (either numerical or non-numerical) was explicitly activated yielded no interaction between the two mappings. As mentioned previously, it is possible that the interaction between both mappings depends on how much the experimental context emphasizes one mapping over the other. By having instructions based on numerical magnitude or physical size, the number/spatial extent mapping might be more activated, preventing the use of a shared representational object. On a related note, previous studies have found that the nature of the number/location mappings, reflected by the SNARC effect, could differ depending on the task (Gevers et al., 2006), with a more categorical association observed in the context of a numerical magnitude judgment task, and a more continuous association in the context of a parity judgment task. It is possible that the two mappings only interact in an experimental context typically eliciting a more continuous number/location mapping.

Second, for an interaction to be observed between the two mappings, another factor could be the level at which the different types of information are being manipulated. When using a magnitude-relevant task, the number/location mapping can only be analyzed by comparing different blocks of trials, corresponding to the different response-key assignments (e.g., “more on the right” vs. “more on the left”). Using a task whereby numerical magnitude is irrelevant, such as in Experiment 2, allows us to analyze the number/location mapping across trials (similarly to the analysis of the number/extent mapping), since the numerical magnitude is independent of the response side. This methodological factor could also contribute to balancing out the weight of each mapping, yielding to their interaction, as observed in Experiment 2. Further studies will be needed to investigate the exact contextual conditions that elicit an interaction between the number/extent and the number/location mappings.

Our results did not show any evidence for an effect of format on the interaction between the two number-space mappings. While Experiment 1 showed an effect of the format of presentation (symbolic vs. non-symbolic) on the number-location mapping, in both experiments the interaction between the two mappings did not differ significantly depending on the format. This could indicate a continuity in the number-space associations between non-symbolic and symbolic representations of magnitude. Developmental studies would help to shed more light on this question.

Altogether, our results support the idea of the existence of a shared spatial representational object with a directionality (from left-to-right in our group of participants), and on which smaller numbers are associated with smaller spatial extents, and larger numbers with larger spatial extents (de Hevia, 2021). In this regard, the mental number line could account both for the number/location and the number/extent mappings. However, and in line with previous studies investigating the SNARC effect in particular (Viarouge et al., 2014), we see that this shared representation can be activated flexibly depending on the experimental context. Thus, while we provide evidence for the existence of a shared representation, our data suggests that its activation is not automatic in any task using numerical stimuli.

The raw data supporting the conclusions of this article will be made available by the authors upon request, without undue reservation.

Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. The patients/participants provided their written informed consent to participate in this study.

AV and MH equally contributed to the conception and design of the study, wrote the first draft of the manuscript, revised it, and approved the submitted version. AV performed the statistical analysis. Both authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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