scholarly journals Space in numerical and ordinal information: A common construct?

2017 ◽  
Vol 3 (2) ◽  
pp. 164-181 ◽  
Author(s):  
Philipp Alexander Schroeder ◽  
Hans-Christoph Nuerk ◽  
Christian Plewnia
Keyword(s):  
Convergent Validity ◽  
Numerical Cognition ◽  
Instrumental Learning ◽  
Verbal Working Memory ◽  
Snarc Effect ◽  
Numerical Magnitude ◽  
Spatial Effects ◽  
Group Level ◽  
Color Classification ◽  
Ordinal Information

Space is markedly involved in numerical processing, both explicitly in instrumental learning and implicitly in mental operations on numbers. Besides action decisions, action generations, and attention, the response-related effect of numerical magnitude or ordinality on space is well documented in the Spatial-Numerical Associations of Response Codes (SNARC) effect. Here, right- over left-hand responses become relatively faster with increasing magnitude positions. However, SNARC-like behavioral signatures in non-numerical tasks with ordinal information were also observed and inspired new models integrating seemingly spatial effects of ordinal and numerical metrics. To examine this issue further, we report a comparison between numerical SNARC and ordinal SNARC-like effects to investigate group-level characteristics and individual-level deductions from generalized views, i.e., convergent validity. Participants solved order-relevant (before/after classification) and order-irrelevant tasks (font color classification) with numerical stimuli 1-5, comprising both magnitude and order information, and with weekday stimuli, comprising only ordinal information. A small correlation between magnitude- and order-related SNARCs was observed, but effects are not pronounced in order-irrelevant color judgments. On the group level, order-relevant spatial-numerical associations were best accounted for by a linear magnitude predictor, whereas the SNARC effect for weekdays was categorical. Limited by the representativeness of these tasks and analyses, results are inconsistent with a single amodal cognitive mechanism that activates space in mental processing of cardinal and ordinal information alike. A possible resolution to maintain a generalized view is proposed by discriminating different spatial activations, possibly mediated by visuospatial and verbal working memory, and by relating results to findings from embodied numerical cognition.

scholarly journals A Minority pulls the sample mean: on the individual prevalence of robust group-level cognitive phenomena – the instance of the SNARC effect

2019 ◽  
Author(s):  
Krzysztof Cipora ◽  
Jean-Philippe van Dijck ◽  
Carrie Georges ◽  
Nicolas Masson ◽  
Silke Melanie Goebel ◽  
...  
Keyword(s):  
Numerical Cognition ◽  
Human Cognition ◽  
Snarc Effect ◽  
Theoretical Issue ◽  
Data Sets ◽  
Group Level ◽  
Scientific Psychology ◽  
Sample Mean ◽  
Individual Level ◽  
The Individual

The aim of cognitive psychology is to obtain insights into human cognition in general. For this purpose, group-studies are typically conducted on representative samples so that the results can be generalized to the population. Using this approach, individual differences in such group-level cognitive phenomena are typically neglected and not much is known about their prevalence at the individual level. Such information is nevertheless important for claims about the universality of phenomena, as in theory, significant effects at the group-level can in principle be driven by a minority of participants. Here we used a uniform analysis of 18 existing data sets revealing a well-replicated phenomenon in numerical cognition: the SNARC (Spatial-Numerical Association of Response Codes) effect, in order to investigate the prevalence of the effect at the individual level. Three methods of analyzing the presence of the effect at the individual level were utilized: one psychometric and two bootstrapping methods. The results show that the group-level SNARC effect is driven by a minority of individuals (≤ 45%) who reveal the effect. This finding demonstrate an important theoretical issue: whether group-level effects really reflect general principles of cognition. We discuss advantages and drawbacks of the present methods and their usefulness for investigating the prevalence of other cognitive phenomena. We posit that testing the presence of robust group-level cognitive effects at the individual level as well as ensuring their reliable measurement is an important step towards integrating two traditionally separate approaches of scientific psychology proposed back in 50’ by Cronbach: experimental and correlational.

EXPRESS: Spatial-numerical associations from a novel paradigm support the Mental Number Line account

2021 ◽  
pp. 174702182110087
Author(s):  
Lauren Aulet ◽  
Sami R Yousif ◽  
Stella Lourenco
Keyword(s):  
Memory Task ◽  
Verbal Working Memory ◽  
Number Line ◽  
Mental Number Line ◽  
Task Demands ◽  
Numerical Magnitude ◽  
The Novel ◽  
Alternative Account ◽  
Subject Design ◽  
Multiple Tasks

Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgments and/or categorical responses. In the novel ‘Where was The Number?’ task, no explicit numerical judgments were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants’ responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

Spatial-numerical associations from a novel paradigm support the mental number line account

2021 ◽  
Author(s):  
Lauren S Aulet ◽  
Sami Ryan Yousif ◽  
Stella F. Lourenco
Keyword(s):  
Memory Task ◽  
Verbal Working Memory ◽  
Number Line ◽  
Mental Number Line ◽  
Task Demands ◽  
Numerical Magnitude ◽  
The Novel ◽  
Alternative Account ◽  
Subject Design ◽  
Multiple Tasks

Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgments and/or categorical responses. In the novel ‘Where was The Number?’ task, no explicit numerical judgments were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants’ responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

scholarly journals Visual Number Beats Abstract Numerical Magnitude: Format-dependent Representation of Arabic Digits and Dot Patterns in Human Parietal Cortex

2015 ◽  
Vol 27 (7) ◽  
pp. 1376-1387 ◽  
Author(s):  
Jessica Bulthé ◽  
Bert De Smedt ◽  
Hans P. Op de Beeck
Keyword(s):  
Activity Pattern ◽  
Numerical Cognition ◽  
Brain Activity ◽  
Activity Patterns ◽  
Brain Regions ◽  
Numerical Magnitude ◽  
Visual Objects ◽  
Arabic Digits ◽  
The One ◽  
Object Cognition

In numerical cognition, there is a well-known but contested hypothesis that proposes an abstract representation of numerical magnitude in human intraparietal sulcus (IPS). On the other hand, researchers of object cognition have suggested another hypothesis for brain activity in IPS during the processing of number, namely that this activity simply correlates with the number of visual objects or units that are perceived. We contrasted these two accounts by analyzing multivoxel activity patterns elicited by dot patterns and Arabic digits of different magnitudes while participants were explicitly processing the represented numerical magnitude. The activity pattern elicited by the digit “8” was more similar to the activity pattern elicited by one dot (with which the digit shares the number of visual units but not the magnitude) compared to the activity pattern elicited by eight dots, with which the digit shares the represented abstract numerical magnitude. A multivoxel pattern classifier trained to differentiate one dot from eight dots classified all Arabic digits in the one-dot pattern category, irrespective of the numerical magnitude symbolized by the digit. These results were consistently obtained for different digits in IPS, its subregions, and many other brain regions. As predicted from object cognition theories, the number of presented visual units forms the link between the parietal activation elicited by symbolic and nonsymbolic numbers. The current study is difficult to reconcile with the hypothesis that parietal activation elicited by numbers would reflect a format-independent representation of number.

Order and Magnitude Share a Common Representation in Parietal Cortex

2009 ◽  
Vol 21 (11) ◽  
pp. 2114-2120 ◽  
Author(s):  
Michael S. Franklin ◽  
John Jonides
Keyword(s):  
Distance Effect ◽  
Number Line ◽  
Judgment Task ◽  
Mental Number Line ◽  
Numerical Magnitude ◽  
Intraparietal Sulcus ◽  
Ordinal Information ◽  
Common Representation ◽  
Distance Effects

The role of the intraparietal sulcus (IPS) in the representation of numerical magnitude is well established. Recently, there has also been speculation that the IPS is involved in the representation of ordinal information as well. These claims, however, overlook the fact that all neuroimaging paradigms in which participants make judgments about either magnitude and/or order result in a behavioral distance effect (i.e., the comparison is easier when the stimuli span a greater distance). This leaves open two possibilities: It may be that activation of the IPS is due to the mechanism that yields distance effects, or it may be that the IPS is involved in the representation of information about both magnitude and order. The current study used fMRI to compare a magnitude task in which participants show distance effects to an order-judgment task that yields reverse-distance effects. The results reveal activation of the IPS for both the magnitude and order tasks that is based on participants' strategies as opposed to the actual distance between the numbers. This leads to the conclusion that the IPS represents a mental number line, and that accessing this line can lead to distance effects when participants compare magnitudes and to reverse-distance effects when participants check for order.

scholarly journals Towards numerical cognition's origin: insights from day-old domestic chicks

2018 ◽  
Vol 373 (1740) ◽  
pp. 20160509 ◽  
Author(s):  
Rosa Rugani
Keyword(s):  
Twentieth Century ◽  
Numerical Cognition ◽  
Domestic Chick ◽  
Ontogenetic Development ◽  
Target Element ◽  
Ordinal Information ◽  
Numerical Abilities ◽  
Domestic Chicks ◽  
Ongoing Work ◽  
Area And Perimeter

Instead of the scepticism on animal numerical understanding that characterized the first half of the twentieth century, in recent decades, a large and increasing body of the literature has shown that adult animals can master a variety of non-symbolic (in the absence of symbols such as mathematical words) numerical tasks. Nonetheless, evidence proving early numerical abilities in non-human animals was sparse. In this paper, I report the ongoing work to investigate numerical cognition in the day-old domestic chick ( Gallus gallus ). Unlike previous studies on adult animals, chicks can be tested very early in life, which gives us the opportunity to discover the origins of numerical comprehension. Here, I discuss studies revealing that day-old domestic chicks can: (i) discriminate between different numbers of objects; (ii) solve rudimentary arithmetic operations; and (iii) use ordinal information, identifying a target element (e.g. the fourth) in a series of identical elements, on the basis of its serial-numerical position. Some of these abilities are number-specific, while others underlie the interplay between number and continuous extents (continuous-quantity cues that covary with number, such as area and perimeter). These data are discussed in terms of ontogenetic development of mathematical comprehension. This article is part of a discussion meeting issue ‘The origins of numerical abilities’.

scholarly journals Turn the beat around: Commentary on “Slow and fast beat sequences are represented differently through space" (De Tommaso & Prpic, 2020, in Attention, Perception, & Psychophysics)

2021 ◽  
Author(s):  
Danielle Wood ◽  
Samuel Shaki ◽  
Martin H. Fischer
Keyword(s):  
Numerical Cognition ◽  
Snarc Effect ◽  
Spatial Mapping ◽  
Spatial Associations ◽  
Response Strategies

AbstractThere has been increasing interest in the spatial mapping of various perceptual and cognitive magnitudes, such as expanding the spatial-numerical association of response codes (SNARC) effect into domains outside of numerical cognition. Recently, De Tommaso and Prpic (Attention, Perception, & Psychophysics, 82, 2765–2773, 2020) reported in this journal that only fast tempos over 104 beats per minute have spatial associations, with more right-sided associations and faster responses for faster tempos. After discussing the role of perceived loudness and possible response strategies, we propose and recommend methodological improvements for further research.

scholarly journals The Force of Numbers: Investigating Manual Signatures of Embodied Number Processing

2021 ◽  
Vol 14 ◽  
Author(s):  
Alex Miklashevsky ◽  
Oliver Lindemann ◽  
Martin H. Fischer
Keyword(s):  
Embodied Cognition ◽  
Grip Force ◽  
Numerical Cognition ◽  
Stimulus Presentation ◽  
Number Line ◽  
Number Processing ◽  
New Technique ◽  
Numerical Magnitude ◽  
Left Hand ◽  
Number Magnitude

The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research.

scholarly journals Cultural factors weaken but do not reverse left-to-right spatial biases in numerosity processing: Data from Arabic and English monoliterates and Arabic-English biliterates

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0261146
Author(s):  
Dominique Lopiccolo ◽  
Charles B. Chang
Keyword(s):  
Snarc Effect ◽  
Numerical Magnitude ◽  
Comparison Task ◽  
Potential Conflict ◽  
Reading Groups ◽  
Task Instructions ◽  
Arabic And English ◽  
Response Biases ◽  
Conceptual Link ◽  
And Task

Directional response biases due to a conceptual link between space and number, such as a left-to-right hand bias for increasing numerical magnitude, are known as the SNARC (Spatial-Numerical Association of Response Codes) effect. We investigated how the SNARC effect for numerosities would be influenced by reading-writing direction, task instructions, and ambient visual environment in four literate populations exemplifying opposite reading-writing cultures—namely, Arabic (right-to-left script) and English (left-to-right script). Monoliterates and biliterates in Jordan and the U.S. completed a speeded numerosity comparison task to assess the directionality and magnitude of a SNARC effect in their numerosity processing. Monoliterates’ results replicated previously documented effects of reading-writing direction and task instructions: the SNARC effect found in left-to-right readers was weakened in right-to-left readers, and the left-to-right group exhibited a task-dependency effect (SNARC effect in the smaller condition, reverse SNARC effect in the larger condition). Biliterates’ results did not show a clear effect of environment; instead, both biliterate groups resembled English monoliterates in showing a left-to-right, task-dependent SNARC effect, albeit weaker than English monoliterates’. The absence of significant biases in all Arabic-reading groups (biliterates and Arabic monoliterates) points to a potential conflict between distinct spatial-numerical mapping codes. This view is explained in terms of the proposed Multiple Competing Codes Theory (MCCT), which posits three distinct spatial-numerical mapping codes (innate, cardinal, ordinal) during numerical processing—each involved at varying levels depending on individual and task factors.

“1-2-3”: Is There a Temporal Number Line?

2008 ◽  
Vol 55 (3) ◽  
pp. 143-150 ◽  
Author(s):  
Dana Müller ◽  
Wolf Schwarz
Keyword(s):  
Number Line ◽  
Congruity Effect ◽  
Snarc Effect ◽  
Numerical Magnitude ◽  
Response Hand ◽  
Semantic Congruity ◽  
Left Response ◽  
The Right ◽  
Semantic Congruity Effect

Abstract. Evidence suggests that numbers are intimately related to space ( Dehaene, Bossini, & Giraux, 1993 ; Hubbard, Piazza, Pinel, & Dehaene, 2005 ). Recently, Walsh (2003) suggested that numbers might also be closely related to time. To investigate this hypothesis we asked participants to compare two digits that were presented in a serial manner, i.e., one after another. Temporally ascending digit pairs (such as 2-3) were responded to faster than temporally descending pairs (3-2). This effect was, in turn, qualified by a local SNARC (spatial numerical association of response codes) effect and a local semantic congruity effect (SCE). Moreover, we observed a global numerical SCE only for temporally descending digit pairs. However, we did not observe a global SNARC effect, i.e., an interaction of numerical magnitude and the right/left response hand. We discuss our results in terms of overlearned forward-associations (“1-2-3”) as formed by our ubiquitous cognitive routines to count off objects or events.

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