Elsevier

Cortex

Volume 134, January 2021, Pages 253-264
Cortex

Research Report
How to trigger and keep stable directional Space–Number Associations (SNAs)

https://doi.org/10.1016/j.cortex.2020.10.020Get rights and content

Abstract

Humans are prone to mentally organise the ascending series of integers according to reading habits so that in western cultures small numbers are positioned to the left of larger ones on a mental number line. Despite 140 years since seminal observations by Sir Francis Galton (Galton, 1880a, b), the functional mechanisms that give rise to directional Space–Number Associations (SNAs) remain elusive. Here, we contrasted three different experimental conditions, each including a different version of a Go/No-Go task with intermixed numerical and arrow-targets (Shaki and Fischer, 2018; Pinto et al., 2019a). We show that directional SNAs are not “all or none” phenomena. We demonstrate that SNAs get progressively less noisy and more stable the more contrasting small/large magnitude-codes and contrasting left/right spatial-codes are explicitly and fully combined in the task set. The analyses of the time–course of space-number congruency effects showed that both the absence and presence of the SNA were independent of the speed of reaction times. In agreement with our original proposal (Aiello et al., 2012), these findings show that conceptualising the ascending series of integers in spatial terms depends on the use of spatial codes in the numerical task at hand rather than on the presence of an inherent spatial dimension in the semantic representation of numbers. This evidence suggests that directional SNAs, like the SNARC effect, are secondary to the primary transfer of spatial response codes to number stimuli, rather than deriving from a primary congruency or incongruence between independent spatial-response and spatial-number codes.

Introduction

Getting acquainted with reading and writing in one's own culture powerfully shapes the ability to conceptualise numbers in spatial terms. Several studies have suggested that the mental representation of the ascending series of integers runs from left-to-right in left-to-right reading cultures and vice versa in right-to-left reading ones (Dehaene et al., 1993; Shaki et al., 2009). This way of representing number magnitudes, the so-called “Mental Number Line” (MNL; Galton, 1880a, Galton, 1880b; Restle, 1970), is especially marked when reading habits are the same for words and numbers, like in western cultures or Palestinians. In contrast, the same effect is less pronounced in cultures, like in Israeli Hebrew speakers, with reading directions running opposite for words and numbers (Shaki et al., 2009). MNLs also do not strictly depend on visual experience, as they occur both in sighted participants and in blind people who have acquired reading direction through the manual modality (for review see Bottini et al., 2015). One crucial issue in the study of the functional origins of MNLs is establishing how deep is the link that reading habits create between space and numbers. Do, as an example, the learned associations between “left” and “small number” and a between “right” and “large number” go so deep that the concept “left” will inherently activate the concept “small number” and vice versa? Are the generation and use of spatially oriented MNLs rooted in these types of co-activation?

The SNARC effect (Dehaene et al., 1993), shows that small numbers are responded faster with key-presses in the left side of space and large numbers with key-presses on the right side. This effect stands as the most reliable and replicated example of the association between space and numbers (Space–Number Association: SNA). According to a taxonomy of SNAs proposed by Cipora, He, & Nuerk, 2020, the SNARC effect falls within the group of “directional” SNAs. These SNAs should be distinguished from “extensional” ones as, for example, the size congruity effect in which judging if the magnitude of an Arabic number in a pair is larger than that of the other number, is facilitated when the first number is also visually larger than the second one. Two types of SNARC effect have been described: the Magnitude Comparison-SNARC and the Parity Judgement-SNARC. In the first case, magnitude codes (smaller/larger than 5) and spatial response codes (left/right) are concomitantly activated to solve the task (e.g., push left if the number is smaller than 5). In the second case, a parity numerical code (odd/even) is combined with a spatial one (left/right) to solve the task (e.g., push left if the number is odd). Current interpretations of the SNARC claim that this effect arises because number magnitude (whether processed explicitly in the Magnitude task or implicitly activated in the Parity task) inherently conveys a left/right spatial code (for review see Wood et al., 2008; Cohen Kadosh et al., 2008; Fattorini et al., 2016). Depending on task instruction, this code can be congruent or incongruent with the spatial code that defines the position of the motor response. When number-spatial and response-spatial codes are congruent, (e.g., push left if the number is lower than 5), reaction times (RTs) are faster than when the two codes are incongruent, (e.g., push left if the number is higher than 5). Although it is currently debated whether the association between spatial and number codes is native (Rugani et al., 2015) or is transmitted in educational settings (Chen and Verguts, 2010), the main interpretative models of the SNARC all assume, in slightly different ways, that the coding of number magnitude automatically triggers the activation of corresponding left/right spatial codes (though see Fischer, 2006, for factors that can determine variations in the top-down strategic control of the effect). According to these models, this happens because: a) depending on their relative magnitude, numbers are inherently positioned in the left or right side of mental space (Dehaene et al., 1993); b) due to hard-wired links between space representation and number representation in the parietal cortex of the two hemispheres, small and large numbers automatically bias attention to the left or to the right, respectively (Chen and Verguts, 2010; Fischer et al., 2003); c) the two contrasting magnitude concepts “small” and “large” are included, respectively, in a culturally acquired higher-order conceptual polarity that also includes spatial concepts like “left”, “down”, “close” (“small”, negative-polarity) and in a contrasting polarity that also includes concepts like “up”, “right”, “far” (“large”, positive-polarity): because of this, it is easier and faster to match the concept “small number” with a “left” manual response and the concept “large number” with a “right” response than vice-versa (Chen and Verguts, 2010; Gevers et al., 2010; Proctor and Cho, 2006; Santens and Gevers, 2008).

At variance with the assumption of an inherent spatial dimension of number magnitude, in the recent past, we have found evidence, that number magnitude has no inherent spatial dimension and that it is the use of contrasting left/right spatial codes required by the task at hand that engenders the mental left-to-right organisation of numbers, whether ordered by magnitude or parity (Doricchi et al., 2005; Aiello et al., 2012; Fattorini et al., 2015; Pinto et al., 2018, 2019a, 2019b). We have proposed that this happens because the left/right conceptual contrast on which response codes are mapped, induces the re-activation of spatially corresponding reading/eye-scanning habits that were acquired in educational settings to inspect and order the ascending series of number magnitudes. Along this line of reasoning, we have argued that, rather than deriving from a primary congruency or incongruence between independent spatial-number and spatial-response codes, directional SNAs, like the SNARC, are based on the primary transfer to number stimuli, of the left/right spatial codes that define the selection of the response (Aiello et al., 2012; Fattorini et al., 2015, 2016; Pinto et al., 2018, 2019a, 2019b). This happens both when the conceptual contrast between left/right spatial codes, regulates the selection of a spatially defined motor response, like in the SNARC task, or the selection of a Go versus a No-Go non-spatial response, like in the Implicit Association Task (Nosek and Banaji, 2001; Fischer and Shaki, 2017; Pinto et al., 2019a).

In a recent study (Pinto et al., 2019a), we have developed on this interpretation. We have addressed the following question: since the space-number association highlighted in SNARC tasks depends on the concomitant use of both left/right spatial-response and small/large number-magnitude codes, does each of these codes used in isolation evoke directional SNAs? To answer this problem, we used variations of a Go/No-Go task that, by recording the timing of simple unimanual responses to intermixed numerical and spatially-informative visual targets, provides a measure of the mental association between numbers and space (see Fischer and Shaki, 2017; Nosek and Banaji, 2001; Shaki, and Fischer, 2018). In different trials of this task, an Arabic digit ranging from “1” to “9” or an arrow that points to the left or the right, acts as a target in the centre of the visual field (see Fig. 1). The presence of an active MNL that runs from left to right is revealed by faster responses when the direction of arrow-targets is congruent with the position that number-targets would occupy on the MNL (e.g., push when an arrow points left and when a number is small), rather than when it is incongruent (e.g., push when an arrow points left and when a number is large). With this task, we were able to show that neither magnitude nor spatial codes used in isolation can evoke the SNA. This was highlighted by the finding that a significant SNA was only generated when the task required to discriminate both the small/large number magnitude and the left/right arrow-direction so that, to this aim, participants have to keep in mind both magnitude and spatial codes (e.g., Go when a number is lower than 5 and when an arrow point to the left). In contrast, no SNA was found when the task required considering only small/large magnitude codes (e.g., Go when a number is lower than 5 and when an arrow is presented) or only left/right spatial codes (Go when an arrow points left and when a number is presented). These results led us to conclude that even when processed explicitly, number magnitude does not automatically convey a spatial code.

Here it is important to note that this conclusion is at variance with that of a study by Shaki and Fischer (2018). These authors adapted the Go/No-Go association task devised by Nosek and Banaji (2001) to the study of the SNA. Based on the result of the second Go/No-Go experiment summarised in their study (Experiment 2, Shaki and Fischer, 2018), these authors proposed that the explicit processing of number magnitude conveys a spatial code while its implicit processing, like in a Parity odd/even task, does not. We have recently argued (Pinto et al., 2019a) that this conclusion might have stemmed from a specific experimental confound in the Go/No-Go task that was used by these authors. In this task Arabic numbers were alternated with horizontal arrows in which the relationship between arrow-direction and colour was fixed (e.g., leftward arrows were all and only red, right-pointing arrows were all and only green). Participants saw alternating arrow- and numeric-targets at central fixation and had to provide Go responses based on specific combinations of arrow colour and number magnitude. The results showed that when participants were required to respond to a particular number-magnitude and a specific arrow-colour, (e.g., push when the number is lower than 5 and when the arrow is red), they were also faster at responding to leftward rather than right-pointing arrows. However, arrows had to be discriminated according to their colour rather than direction, so that, task instructions activated no spatial code. Though these results seem to suggest that processing a specific number magnitude, “small”, automatically speeds up the processing of directional stimuli characterised by a congruent spatial code, “left”, we have remarked (Pinto et al., 2019a) that in the experiment by Shaki and Fischer (2018) the systematic association of task-relevant colour codes with a specific arrow direction might have introduced spurious effects. It is easy to argue that when a healthy observer is asked to provide a Go response only to red arrows and red arrows are all and only directed to the left, the observer quickly learns that “red” is equivalent to “left” so that the instruction “push when the number is lower than 5 and when the arrow is red” becomes equal to “push when the number is lower than 5 and the arrow points left”, that is to an instruction that, like in conventional SNARC tasks, includes both magnitude and spatial codes. In our study (Pinto et al., 2019a) we have demonstrated that when no systematic relationship between arrow direction and arrow colour is present, the joint detection of number magnitude and arrow colour, does not produce magnitude-space congruency effects. For example, the detection of numbers lower than 5 does not speeds-up the detection of arrows pointing to the left.

In the present investigation, we wished to expand further on these findings and explore more in-depth two relevant issues. First, we investigated to which degree not only the significance but also the stability and reliability of the SNA depends on the full combination of contrasting left/right spatial and contrasting small/large number magnitude codes during the performance of a numerical task. Recent failures in replicating specific examples of SNA, like the Attentional-SNARC (for reviews and new empirical data see Pellegrino et al., 2019; Colling et al., 2020), point out the importance of ascertaining the reliability of SNAs that are observed in specific tasks. To this aim, in a single large experiment, we contrasted three different experimental conditions. Across these conditions, we gradually increased the integrated use of spatial and number magnitude codes. Each of these experimental conditions included a different variation of a Go/No-Go task with alternating Arabic numbers and arrow targets presented at central fixation. In Experimental Condition 1 (ExpC1), we asked healthy adult participants to contrast the small/large magnitude of numbers explicitly, thus responding only to small or large numbers, without contrasting the left/right spatial code that defined the direction of arrows, or vice-versa. In Experimental Condition 2 (ExpC2), we asked participants to explicitly contrast the small/large magnitude of numbers while classifying the direction of arrows according to a superordinate semantic code that included, without explicitly activating, the left/right direction of arrows (i.e., “responding only to horizontal arrows”: a horizontal arrow can be oriented only in the left or in the right direction). Vice versa in a second task included in the same experimental condition, participants were asked to contrast the left/right direction of arrows while classifying numbers according to superordinate semantic code that included, without explicitly activating, the small/large magnitude of numbers (i.e., “responding only to numbers that were different from 5”, that is only to numbers that are smaller or larger than 5). In Experimental Condition 3 (ExpC3), task instructions activated the full combination of contrasting small/large magnitude with contrasting left/right spatial codes, (e.g., responding only to numbers smaller than 5 and only to left-pointing arrows). In this way, we parametrically manipulated the progressive and integrated use of spatial and magnitude codes in the task.

A second important issue in the study of directional SNAs is the time-course of space-number congruency effects. It is well established that stimulus-response congruency effects like the SNARC (Gevers et al., 2005) or the Simon effect (Rubichi et al., 1997), get larger and significant with increasing reaction times. Therefore, in a series of ad-hoc analyses (see Methods), we explored the time course of the space-number congruency effects that were elicited in the three experimental conditions of our study.

Section snippets

General method

In this section, we report how we determined our sample size, all data exclusions, all inclusion/exclusion criteria, whether inclusion/exclusion criteria were established prior to data analysis, all manipulations, and all measures in the study.

Discussion

In a previous investigation, we have identified in the integrated use of contrasting left/right spatial and contrasting small/large number-magnitude codes, the condition that gives rise to significant directional SNAs (Pinto et al., 2019a). Here we investigated more in-depth how the progressive integration of these codes affects the significance and reliability of the SNA. We also explored the time-course of directional SNAs, by testing whether the presence and strength of directional SNAs

Author contributions

F.D, M.P., and M.P developed the study concept. All authors contributed to the study design. M.P., M.P., F.M. and S.L. collected and analysed data. F.D., M.P. and V.C. drafted the manuscript. All co-authors provided critical revisions to the initial version of the manuscript.

Data accessibility

The conditions of our ethics approval do not permit public archiving of anonymised study data. Readers seeking access to the data should contact the corresponding author Prof. Fabrizio Doricchi ([email protected]) or the local ethics committee at IRCCS Fondazione Santa Lucia, Roma – Italy. Access will be granted to named individuals in accordance with ethical procedures governing the reuse of sensitive data. There are no specific conditions that the requestors must meet to obtain

Credit author statement

Mario Pinto: Conceptualization, Methodology, Investigation, Formal analysis and Writing Original Draft, Writing- Reviewing and Editing. Michele Pellegrino: Conceptualization, Software, Investigation and Formal analysis. Fabio Marson: Software, Investigation. Stefano Lasaponara: Investigation, Resources. Vincenzo Cestari: Writing - Review & Editing, Resources. Marianna D'Onofrio: Funding acquisition, Resources. Fabrizio Doricchi: Conceptualization, Methodology, Supervision, Writing - Original

Open practices

The study in this article earned an Open Materials badge for transparent practices. Stimuli, data and software are available upon request.

Acknowledgements

We wish to thank Sarah Shomstein, Guido Marco Cicchini, Roberto Bottini and Davide Crepaldi for useful suggestions on a first draft of the manuscript. We thank Giada Baldo, Jessica Callà, Valentina Galiotta, Claudia Golser and Alessandra Martucci for help in data collection. This work was supported by grants PRIN 2017 to F.D. (project code 2017XBJN4F), by a grant Ricerche di Ateneo 2018 to F.D. and V.C. and a by grant Fondazione Terzo Pilastro to F.D., M.P. and M. D’O.

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