The origins and structure of quantitative concepts

Bonn, Cory D.; Cantlon, Jessica F.

doi:10.1080/02643294.2012.707122

Cited by 35 publications

(34 citation statements)

References 147 publications

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“…These observations are consistent with the existence of a shared analog code or generalized magnitude representation (Holyoak & Glass, 1978; Gallistel & Gelman, 2000; Walsh, 2003; Pinel, Piazza, Le Bihan, & Dehaene, 2004; see Cohen Kadosh, Lammertyn, & Izard, 2008; Bueti & Walsh, 2009; Cantlon, Platt, & Brannon, 2009; Bonn & Cantlon, 2012; and Lourenco, 2015 for extensive reviews). However, the shared-code hypothesis remains underspecified because the existing data has not revealed much about the code’s internal structure.…”

Section: Introductionsupporting

confidence: 75%

“…From this point of view, a single magnitude system may be unsuitable for solving many different types of information-integration problems. Subjects may use all of the above representations and computational strategies across the different tasks they encounter in the environment, including ratio-scaled comparisons, direct mappings between absolute magnitudes, statistical inference in cue integration, and analogical reasoning (Bonn & Cantlon, 2012). Thus, the so-called “generalized magnitude system” may not be one coherent representational system, but rather a set of relational mapping phenomena.…”

Section: Discussionmentioning

confidence: 99%

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Spontaneous, modality-general abstraction of a ratio scale

Bonn

Cantlon

2017

Cognition

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The existence of a generalized magnitude system in the human mind and brain has been studied extensively but remains elusive because it has not been clearly defined. Here we show that one possibility is the representation of relative magnitudes via ratio calculations: ratios are a naturally dimensionless or abstract quantity that could qualify as a common currency for magnitudes measured on vastly different psychophysical scales and in different sensory modalities like size, number, duration, and loudness. In a series of demonstrations based on comparisons of item sequences, we demonstrate that subjects spontaneously use knowledge of inter-item ratios within and across sensory modalities and across magnitude domains to rate sequences as more or less similar on a sliding scale. Moreover, they rate ratio-preserved sequences as more similar to each other than sequences in which only ordinal relations are preserved, indicating that subjects are aware of differences in levels of relative-magnitude information preservation. The ubiquity of this ability across many different magnitude pairs, even those sharing no sensory information, suggests a highly general code that could qualify as a candidate for a generalized magnitude representation.

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Section: Introductionsupporting

confidence: 75%

Section: Discussionmentioning

confidence: 99%

Spontaneous, modality-general abstraction of a ratio scale

Bonn

Cantlon

2017

Cognition

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“…Recently, a growing body of results has supported the idea that the left-right axis is a relevant spatial reference in order to metaphorically understand continuous abstract concepts. Indeed, mapping between such an axis and concepts such as numbers, time, and even politics is now strongly supported (Casasanto & Boroditsky, 2008;Dehaene, Bossini, & Giraux, 1993;Oppenheimer & Trail, 2010;Ren, Nicholls, Ma, & Chen, 2011; for recent reviews, see Bonn & Cantlon, 2012;Dijkstra, Eerland, Zijlmans, & Post, 2014;Winter et al, 2015). Together with our present results regarding the concept of valence, we assume the possibility that humans could have a kind of general tendency to represent continuous abstract concepts via the metaphor of a left-right continuum.…”

Section: Discussionsupporting

confidence: 50%

A continuous mapping between space and valence with left- and right-handers

et al. 2015

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In this research, we examined whether emotional valence could correspond to a continuous lateral bias in space, according to a mental metaphor that establishes the mapping between a concrete domain (space) and an abstract one (valence). Because acting with one's dominant hand is associated with fluency and positive valence (the bodily specificity hypothesis, or BSH), we asked strong right-and left-handers to perform two spatial location tasks using emotional faces with seven levels of valence. We hypothesized and showed through two studies that, according to the BSH, extreme valenced stimuli (as compared to moderate and weak ones) would be located more at the extremity of a horizontal line, according to the correspondences between handedness and the different valences of the stimuli. This research establishes that spatial and continuous mapping of emotions was obtained while controlling for motivational direction.

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“…Brightness, while not usually described as being part of this group of dimensions, can elicit similar kinds of interference at the perceptual level (Xuan et al, 2007; Westheimer, 2008). In a recent review, Bonn and Cantlon (2012) described two main models to account for the links between the representational systems for multiple continuous dimensions of magnitude. On one hand, one can postulate the existence of an amodal (“adimensional,” as suggested by the authors) higher level of representation.…”

Section: Discussionmentioning

confidence: 99%

The role of numerical magnitude and order in the illusory perception of size and brightness

Viarouge

Hevia

2013

Front. Psychol.

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Processing magnitudes constitutes a common experience across multiple dimensions, for example when one has to compare sizes, duration, numbers, sound height or loudness. From a cognitive point of view, however, it is still unclear whether all these experiences rely on a common system, or on distinct systems, with more or less strong associations. One particularly striking way of observing such interference between the spatial and numerical dimensions consists in eliciting a bias in size judgment through the mere perception of irrelevant numerical stimuli. In such experimental context though, two questions remain open. First, it is still unknown whether the direction of the bias is related to the magnitude of the number presented, or to their position in an ordinal sequence, and thus could be elicited by other non-numerical ordinal sequences such as letters of the alphabet. Second, it is still unclear whether the observed interactions generalize to other continuous dimension of magnitude such as brightness. In the study reported here, both letters and numbers were used in a size- and a brightness-reproduction task. We observed a dissociation between the two types of stimuli when reproducing size, the illusion being elicited solely by numbers. When reproducing brightness, however, neither the letters nor the numbers elicited a bias. These findings suggest that, while only numerical magnitude, and not letters, elicits a bias in size perception, the concurrent processing of magnitude and brightness does not bring about the same illusion, supporting the idea of a relative independence in the processing of these two dimensions.

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The origins and structure of quantitative concepts

Cited by 35 publications

References 147 publications

Spontaneous, modality-general abstraction of a ratio scale

Spontaneous, modality-general abstraction of a ratio scale

A continuous mapping between space and valence with left- and right-handers

The role of numerical magnitude and order in the illusory perception of size and brightness

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