Conjoint measurement of physical size and numerical magnitude: Numerals do not automatically activate their semantic meaning

Humans not only process and compare magnitude information such as size, duration, and number perceptually, but they also communicate about these properties using language. In this respect, a relevant class of lexical items are so-called scalar adjectives like ‘big’, ‘long’, ‘loud’, etc. which refer to magnitude information. It has been proposed that humans use an amodal and abstract representation format shared by different dimensions, called the generalized magnitude system (GMS). In this paper, we test the hypothesis that scalar adjectives are symbolic references to GMS representations, and, therefore, GMS gets involved in processing their meaning. Previously, a parallel hypothesis on the relation between number symbols and GMS representations has been tested with the size congruity paradigm. The results of these experiments showed interference between the processing of number symbols and the processing of physical (font-) size. In the first three experiments of the present study (total N=150), we used the size congruity paradigm and the same/different task to look at the potential interaction between physical size magnitude and numerical magnitude expressed by number words. In the subsequent three experiments (total N=149), we looked at a parallel potential interaction between physical size magnitude and scalar adjective meaning.

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Modeling the latent structure of individual differences in the numerical size-congruity effect

10.31234/osf.io/4b9rs ◽

2020 ◽

Author(s):

Thomas J. Faulkenberry ◽

Kristen Bowman

Keyword(s):

Individual Differences ◽

Numerical Cognition ◽

Congruity Effect ◽

Numerical Magnitude ◽

Data Sets ◽

Comparison Task ◽

Physical Size ◽

The Individual ◽

Size Congruity Effect ◽

Individual Size

When people are asked to choose the physically larger of a pair of numerals, they are often slower when relative physical size is incongruent with numerical magnitude. This size-congruity effect is usually assumed as evidence for automatic activation of numerical magnitude. In this paper, we apply the methods of Haaf and Rouder (2017) to look at the size-congruity effect through the lens of individual differences. Here, we simply ask whether everyone exhibits the effect. We develop a class of hierarchical Bayesian mixed models with varying levels of constraint on the individual size- congruity effects. The models are then compared via Bayes factors, telling us which model best predicts the observed data. We then apply this modeling technique to three data sets. In all three data sets, the winning model was one in which the size-congruity effect was constrained to be positive. This indicates that, at least in a physical comparison task with numerals, everyone exhibits a positive size-congruity effect. We discuss these results in the context of measurement fidelity and theory-building in numerical cognition.

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Symbols are special: An fMRI adaptation study of symbolic, nonsymbolic and non-numerical magnitude processing in the human brain

10.31234/osf.io/xw2fq ◽

2019 ◽

Author(s):

H Moriah Sokolowski ◽

Zachary Hawes ◽

Lien Peters ◽

Daniel Ansari

Keyword(s):

Human Brain ◽

Processing System ◽

Number Processing ◽

Numerical Magnitude ◽

Physical Size ◽

Parietal Lobes ◽

Magnitude Processing ◽

The Right ◽

Fmri Adaptation ◽

Symbolic Number

Humans have the unique ability to represent and manipulate symbols. It is widely believed that this ability is rooted in an evolutionarily ancient system used to process nonsymbolic quantities in the human brain. In the current study, we used an fMRI adaptation paradigm to isolate the representations of symbols, quantities, and physical size in forty-five human adults. Results indicate that the neural correlates supporting symbolic number processing are entirely distinct from those supporting nonsymbolic magnitude processing. At the univariate level, symbolic number processing is associated with activation in the left inferior parietal lobule, whereas the processing of nonsymbolic magnitudes (both quantity and physical size), relates to activation in the right intraparietal sulcus. At the multivariate level, normalized patterns of activation for symbolic number processing exhibit a dissimilar pattern of activation compared to nonsymbolic magnitude processing in both the left and right parietal lobes. Additionally, the patterns of activation that associate with quantity and physical size are practically indistinguishable from one another. These findings challenge the longstanding belief that the culturally acquired ability to conceptualize symbolic numbers is rooted in an evolutionarily ancient system for nonsymbolic magnitude processing. Moreover, these data reveal that the system used to process nonsymbolic numbers may actually be a general magnitude processing system used to process numerical and non-numerical magnitudes. These findings highlight the need for the field to shift away from exploring how symbols are grounded in analog nonsymbolic representations, and toward more complex questions related to the neural consequences of learning symbolic numbers.

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Processing symbolic magnitude information conveyed by number words and by scalar adjectives

10.31234/osf.io/gwfrz ◽

2020 ◽

Author(s):

Arnold Kochari

Keyword(s):

Potential Interaction ◽

Numerical Magnitude ◽

Font Size ◽

Total N ◽

Physical Size ◽

Number Words ◽

Scalar Adjective ◽

Reverse Situation ◽

The One ◽

Scalar Adjectives

Humans not only process and compare magnitude information such as size, duration, and number perceptually, but they also communicate about these properties using language. In this respect, a relevant class of lexical items are so-called scalar adjectives like ‘big’, ‘long’, ‘loud’, etc. which refer to magnitude information. It has been proposed that humans use an amodal and abstract representation format shared by different dimensions, called the generalized magnitude system (GMS). In this paper, we test the hypothesis that scalar adjectives are symbolic references to GMS representations, and, therefore, GMS gets involved in processing their meaning. Previously, a parallel hypothesis on the relation between number symbols and GMS representations has been tested with the size congruity paradigm. The results of these experiments showed interference between the processing of number symbols and the processing of physical (font-) size. In the first three experiments of the present study (total N=150), we used the size congruity paradigm and the same/different task to look at the potential interaction between physical size magnitude and numerical magnitude expressed by number words. In the subsequent three experiments (total N=149), we looked at a parallel potential interaction between physical size magnitude and scalar adjective meaning. In the size congruity paradigm we observed interference between the processing of the numerical value of number words and the meaning of scalar adjectives, on the one hand, and physical (font-) size, on the other had, when participants had to judge the number words or the adjectives (while ignoring physical size). No interference was obtained for the reverse situation, i.e. when participants judged the physical font size (while ignoring numerical value or meaning). The results of the same/different task for both number words and scalar adjectives strongly suggested that the interference that was observed in the size congruity paradigm was likely due to a response conflict at the decision stage of processing rather than due to the recruitment of GMS representations. Taken together, it can be concluded that the size congruity paradigm does not provide evidence in support the hypothesis that GMS representations are used in the processing of number words or scalar adjectives. Nonetheless, the hypothesis we put forward about scalar adjectives is still is a promising potential line of research. We make a number of suggestions for how this hypothesis can be explored in future studies.

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On the Internal Representation of Numerical Magnitude and Physical Size

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000235 ◽

2014 ◽

Vol 61 (2) ◽

pp. 149-163 ◽

Cited By ~ 10

Author(s):

Daniel Fitousi

Keyword(s):

Signal Detection ◽

Signal Detection Theory ◽

Numerical Cognition ◽

Internal Representation ◽

Numerical Magnitude ◽

Semantic Relationship ◽

Physical Size ◽

General Recognition Theory ◽

Recognition Theory ◽

General Recognition

A nascent idea in the numerical cognition literature – the analogical hypothesis ( Pinel, Piazza, Bihan, & Dehaene, 2004 ) – assumes a common noisy code for the representation of symbolic (e.g., numerals) and nonsymbolic (e.g., numerosity, physical size, luminance) magnitudes. The present work subjected this assumption to various tests from the perspective of General Recognition Theory (GRT; Ashby & Townsend, 1986 ) – a multidimensional extension of Signal Detection Theory ( Green & Swets, 1966 ). The GRT was applied to the dimensions of numerical magnitude and physical size with the following goals: (a) characterizing the internal representation of these dimensions in the psychological space, and (b) assessing various types of (in)dependence and separability governing the perception of these dimensions. The results revealed various violations of independence and separability with Stroop incongruent, but not with Stroop congruent stimuli. The outcome suggests that there are deep differences in architecture between Stroop congruent and incongruent stimuli that reach well beyond the semantic relationship involved.

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Dorsal striatum mediates cognitive control, not cognitive effort per se, in decision-making: an event-related fMRI study

Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques ◽

10.1017/cjn.2015.94 ◽

2015 ◽

Vol 42 (S1) ◽

pp. S16-S16

Author(s):

BD Robertson ◽

NM Hiebert ◽

KN Seergobin ◽

AM Owen ◽

PA MacDonald

Keyword(s):

Decision Making ◽

Cognitive Control ◽

Response Times ◽

Dorsal Striatum ◽

Error Rates ◽

Cognitive Effort ◽

Blood Oxygenation ◽

Numerical Magnitude ◽

Physical Size ◽

Per Se

Background: Whether the dorsal striatum (DS) mediates cognitive control or cognitive effort per se in decision-making is unclear because as cognitive control requirements of a task intensify, cognitive effort requirements increase proportionately. We implemented a task that disentangled cognitive control and cognitive effort to specify the function DS mediates in decision-making. Methods: Sixteen healthy young adults completed a number Stroop task with simultaneous blood-oxygenation-level-dependent response (BOLD) measurement. Participants selected the physically larger number of a pair. Discriminating smaller physical size differences increases cognitive effort, but does not demand greater cognitive control. We also investigated the effect of interdimensional conflict between physical size and numerical magnitude. Selections in this incongruent case are more cognitively effortful and require greater cognitive control to suppress responding to the irrelevant dimension. Enhancing cognitive effort or cognitive control requirements increases response times and error rates. Results: Behavioural interference occurred for both conditions; however, DS BOLD signal only correlated with interference due to increased cognitive control requirements. DS was not preferentially activated for discriminations of smaller relative to larger physical size differences between number pairs, even when using liberal statistical criteria. Conclusions: Our findings support the increasingly accepted notion that DS mediates cognitive control specifically and does not index cognitive effort per se.

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The Flip Side of the Auditory Spatial Selection Benefit

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000274 ◽

2015 ◽

Vol 62 (1) ◽

pp. 66-74 ◽

Cited By ~ 2

Author(s):

Iring Koch ◽

Vera Lawo

Keyword(s):

Task Switching ◽

Auditory Task ◽

Numerical Magnitude ◽

Attention Shifting ◽

Gender Selection ◽

Spatial Selection ◽

Number Words ◽

Switch Costs ◽

Mixing Costs ◽

Experimental Group

In cued auditory task switching, one of two dichotically presented number words, spoken by a female and a male, had to be judged according to its numerical magnitude. One experimental group selected targets by speaker gender and another group by ear of presentation. In mixed-task blocks, the target-defining feature (male/female vs. left/right) was cued prior to each trial, but in pure blocks it remained constant. Compared to selection by gender, selection by ear led to better performance in pure blocks than in mixed blocks, resulting in larger “global” mixing costs for ear-based selection. Selection by ear also led to larger “local” switch costs in mixed blocks, but this finding was partially mediated by differential cue-repetition benefits. Together, the data suggest that requirements of attention shifting diminish the auditory spatial selection benefit.

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