scholarly journals Improvised Numerals Rely on 1-to-1 Correspondence

2021 ◽  
Author(s):  
Sebastian Holt ◽  
David Barner ◽  
Judith Fan
Keyword(s):  
Mathematical Reasoning ◽  
Perceptual Processing ◽  
Third Party ◽  
Systematic Bias ◽  
Cognitive Constraints ◽  
Symbolic Representations ◽  
Number Systems ◽  
Iconic Representations ◽  
Visual Properties ◽  
Processing Mechanisms

Symbolic representations of number are instrumental to mathematical reasoning and many aspects of social organization. What explains their emergence in human cultures? To understand how functional and cognitive constraints impact people’s communication about number, we used a drawing-based reference game to investigate how human dyads coordinated to form novel number systems. We found a systematic bias towards symbols exploiting 1-to-1 correspondence to objects in visual arrays, and that this strategy was contingent on the communicative relevance of number. Moreover, the meaning of these symbols was transparent to third party observers not present during their production. Finally, model-based analyses of these symbols' visual properties suggest that the ability to decode exact quantity from them may rely on perceptual processing mechanisms beyond those sufficient for object recognition. These findings contribute to our understanding of how both communicative need and capacity for visual abstraction constrain the emergence of iconic representations of exact number.

scholarly journals Faces in commonly experienced configurations enter awareness faster due to their curvature relative to fixation

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e1565 ◽  
Author(s):  
Pieter Moors ◽  
Johan Wagemans ◽  
Lee de-Wit
Keyword(s):  
Fusiform Face Area ◽  
General Shape ◽  
Continuous Flash Suppression ◽  
Face Area ◽  
Contrast Adaptation ◽  
Neuroimaging Study ◽  
Face Stimuli ◽  
High Level ◽  
Visual Properties ◽  
Processing Mechanisms

The extent to which perceptually suppressed face stimuli are still processed has been extensively studied using the continuous flash suppression paradigm (CFS). Studies that rely on breaking CFS (b-CFS), in which the time it takes for an initially suppressed stimulus to become detectable is measured, have provided evidence for relatively complex processing of invisible face stimuli. In contrast, adaptation and neuroimaging studies have shown that perceptually suppressed faces are only processed for a limited set of features, such as its general shape. In this study, we asked whether perceptually suppressed face stimuli presented in their commonly experienced configuration would break suppression faster than when presented in an uncommonly experienced configuration. This study was motivated by a recent neuroimaging study showing that commonly experienced face configurations are more strongly represented in the fusiform face area. Our findings revealed that faces presented in commonly experienced configurations indeed broke suppression faster, yet this effect did not interact with face inversion suggesting that, in a b-CFS context, perceptually suppressed faces are potentially not processed by specialized (high-level) face processing mechanisms. Rather, our pattern of results is consistent with an interpretation based on the processing of more basic visual properties such as convexity.

A simulation study on word order bias

2009 ◽  
Vol 10 (1) ◽  
pp. 51-75 ◽  
Author(s):  
Tao Gong ◽  
James W. Minett ◽  
William S-Y. Wang
Keyword(s):  
Language Processing ◽  
Word Order ◽  
Universal Grammar ◽  
Local Order ◽  
Global Order ◽  
Cognitive Constraints ◽  
Basic Word ◽  
Multi Agent ◽  
Processing Mechanisms ◽  
Trigger Bias

The majority of the extant languages have one of three dominant basic word orders: SVO, SOV or VSO. Various hypotheses have been proposed to explain this word order bias, including the existence of a universal grammar, the learnability imposed by cognitive constraints, the descent of modern languages from an ancestral protolanguage, and the constraints from functional principles. We run simulations using a multi-agent computational model to study this bias. Following a local order approach, the model simulates individual language processing mechanisms in production and comprehension. The simulation results demonstrate that the semantic structures that a language encodes can constrain the global syntax, and that local syntax can help trigger bias towards the global order SOV/SVO (or VOS/OVS).

scholarly journals Changes of Causal Attribution by a Co-actor in Situations of Obvious Causality

2021 ◽  
Vol 11 ◽  
Author(s):  
Kazuki Hayashida ◽  
Yu Miyawaki ◽  
Yuki Nishi ◽  
Shu Morioka
Keyword(s):  
Causal Attribution ◽  
Social Contexts ◽  
Perceptual Processing ◽  
Third Party ◽  
Responsibility Attribution ◽  
Experimental Conditions ◽  
External Attribution ◽  
Harm Condition ◽  
Potential Diffusion ◽  
Diffusion Of Responsibility

In social contexts, people are responsible for their actions and outcomes. Diffusion of responsibility is a well-known social phenomenon: people feel less responsible when performing an action with co-actors than when acting alone. In previous studies, co-actors reduced the participant’s responsibility attribution by making the cause of the outcomes ambiguous. Meanwhile, it is unclear whether the presence of co-actors creates diffusion of responsibility even in situations where it is “obvious” that both oneself and the co-actor are the causes of an outcome. To investigate this potential diffusion of responsibility, we used a temporal binding (TB) task as a measure of causal attribution. Low TB effects indicate the enhancement of external attribution (i.e., diffusion of responsibility) in perceptual processing for the action and outcomes. To investigate the influence of presence of a co-actor on causal attribution, participants were required to act under two experimental conditions: an ALONE condition (participant only) or a TOGETHER condition (with a co-actor). The only difference between the two conditions was whether the actions were shared. In addition, to make participants feel responsible, they were induced to feel guilt. In the High-harm condition, participants gave a financial reduction to a third party. When guilt was induced, participants showed lower TB effects in the TOGETHER condition compared to the ALONE condition. Our study suggests that actions with a co-actor change causal attributions even though the causes of the outcome are obvious. This may have implications for understanding diffusion of responsibility in inhumane situations.

scholarly journals Causal events enter awareness faster than non-causal events

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e2932 ◽  
Author(s):  
Pieter Moors ◽  
Johan Wagemans ◽  
Lee de-Wit
Keyword(s):  
Experimental Methods ◽  
Perceptual Processing ◽  
Interocular Suppression ◽  
Continuous Flash Suppression ◽  
Perception Of Causality ◽  
Suppression Technique ◽  
Visual Phenomena ◽  
Sensory Evidence ◽  
Low Levels ◽  
Visual Properties

Philosophers have long argued that causality cannot be directly observed but requires a conscious inference (Hume, 1967). Albert Michotte however developed numerous visual phenomena in which people seemed to perceive causality akin to primary visual properties like colour or motion (Michotte, 1946). Michotte claimed that the perception of causality did not require a conscious, deliberate inference but, working over 70 years ago, he did not have access to the experimental methods to test this claim. Here we employ Continuous Flash Suppression (CFS)—an interocular suppression technique to render stimuli invisible (Tsuchiya & Koch, 2005)—to test whether causal events enter awareness faster than non-causal events. We presented observers with ‘causal’ and ‘non-causal’ events, and found consistent evidence that participants become aware of causal events more rapidly than non-causal events. Our results suggest that, whilst causality must be inferred from sensory evidence, this inference might be computed at low levels of perceptual processing, and does not depend on a deliberative conscious evaluation of the stimulus. This work therefore supports Michotte’s contention that, like colour or motion, causality is an immediate property of our perception of the world.

scholarly journals Non-symbolic numerosities do not automatically activate spatial–numerical associations: Evidence from the SNARC effect

2019 ◽  
Vol 73 (2) ◽  
pp. 295-308
Author(s):  
Alexandra A Cleland ◽  
Kathryn Corsico ◽  
Kirstin White ◽  
Rebecca Bull
Keyword(s):  
Surface Area ◽  
Visual Cues ◽  
Full Range ◽  
Total Surface Area ◽  
Snarc Effect ◽  
Spatial Associations ◽  
Symbolic Representations ◽  
Canonical Representations ◽  
Visual Properties

The SNARC (spatial–numerical association of response codes) effect is the finding that people are generally faster to respond to smaller numbers with left-sided responses and larger numbers with right-sided responses. The SNARC effect has been widely reported for responses to symbolic representations of number such as digits. However, there is mixed evidence as to whether it occurs for non-symbolic representations of number, particularly when magnitude is irrelevant to the task. Mitchell et al. reported a SNARC effect when participants were asked to make orientation decisions to arrays of one-to-nine triangles (pointing upwards vs. pointing downwards) and concluded that SNARC effects occur for non-symbolic, non-canonical representations of number. They additionally reported that this effect was stronger in the subitising range. However, here we report four experiments that do not replicate either of these findings. Participants made upwards/inverted decisions to one-to-nine triangles where total surface area was either controlled across numerosities (Experiments 1, 2, and 4) or increased congruently with numerosity (Experiment 3). There was no evidence of a SNARC effect either across the full range or within the subset of the subitising range. The results of Experiment 4 (in which we presented the original stimuli of Mitchell et al.) suggested that visual properties of non-symbolic displays can prompt SNARC-like effects driven by visual cues rather than numerosity. Taken in the context of other recent findings, we argue that non-symbolic representations of number do not offer a direct and automatic route to numerical–spatial associations.

scholarly journals Direct Punishment and Indirect Reputation-Based Tactics to Intervene Against Offenses

2021 ◽  
Author(s):  
Catherine Molho ◽  
Junhui Wu
Keyword(s):  
Decision Rules ◽  
Partner Choice ◽  
Third Party ◽  
Social Functions ◽  
Third Party Intervention ◽  
Emotional Factors ◽  
Interdependent Relationships ◽  
Processing Mechanisms ◽  
Benefits And Costs

Punishment and reputation-based mechanisms play a major role in supporting the evolution of human cooperation. Theoretical accounts and field observations suggest that humans use multiple tactics to intervene against offenses—including confrontation, gossip, and ostracism—which have unique benefits and costs. Here, we draw a distinction between direct punishment tactics (i.e., physical and verbal confrontation) and indirect reputation-based tactics (i.e., gossip and ostracism). Based on this distinction, we sketch the common and unique social functions that different tactics are tailored to serve and describe information-processing mechanisms that potentially underlie decisions concerning how to intervene against offenses. We propose that decision rules guiding direct and indirect tactics should weigh information about the benefits of changing others’ behavior versus the costs of potential retaliation. Based on a synthesis of existing evidence, we highlight the role of situational, relational, and emotional factors in motivating distinct punishment tactics. We suggest that delineating between direct and indirect tactics can inform debates about the prevalence and functions of punishment, and the reputational consequences of third-party intervention against offenses. We emphasize the need to study how people use reputation-based tactics for partner recalibration and partner choice, within interdependent relationships and social networks, and in daily life situations.

scholarly journals Development of the model of protected cross-border information interaction

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
R. G. Biyashev ◽  
S. E. Nyssanbayeva ◽  
Ye. Y. Begimbayeva
Keyword(s):  
Digital Signature ◽  
Information Exchange ◽  
High Reliability ◽  
Integrated System ◽  
Third Party ◽  
Integration System ◽  
Cross Border ◽  
Number Systems ◽  
Digital Signature Algorithm ◽  
Information Interaction

Abstract This article investigates a proposed model of cross-border exchange and information security in the cross-border interaction in the integration system. A structural scheme of protected cross-border information exchange is proposed. Cross-border interaction of sides for information exchange in the integrated system is provided by the creation and use of the integration segment and national segments. The main tasks of a trusted third party are formulated. The model of sides’ interaction scheme of the integration system using the integration gateway is presented. In this paper, a model of modified nonconventional digital signature system based on the scheme of the Digital Signature Algorithm and nonpositional polynomial number systems (NPNs) are described. Application of NPNs allows creating effective cryptographic systems of high reliability, which enables the confidentiality, authentication, integrity of stored and transmitted information.

scholarly journals Non-symbolic number does not automatically activate spatial-numerical associations: Evidence from the SNARC effect.

2018 ◽  
Author(s):  
Alexandra Alice Cleland ◽  
Kathryn Corsico ◽  
Kirstin White ◽  
Rebecca Bull
Keyword(s):  
Surface Area ◽  
Visual Cues ◽  
Full Range ◽  
Total Surface Area ◽  
Snarc Effect ◽  
Symbolic Representations ◽  
Subitizing Range ◽  
Canonical Representations ◽  
Visual Properties ◽  
Symbolic Number

The SNARC (spatial numerical association of response codes) effect is the finding that people are generally faster to respond to smaller numbers with left-sided responses and larger numbers with right-sided responses. The SNARC effect has been widely reported for responses to symbolic representations of number such as digits. However, there is mixed evidence as to whether it occurs for non-symbolic representations of number, particularly when magnitude is irrelevant to the task. Mitchell et al. (2012) reported a SNARC effect when participants were asked to make orientation decisions to arrays of one-to-nine triangles (pointing upwards versus pointing downwards) and concluded that SNARC effects occur for non-symbolic, non-canonical representations of number. They additionally reported that this effect was stronger in the subitizing range. However, here we report four experiments that do not replicate either of these findings. Participants made upwards / inverted decisions to one-to-nine triangles where total surface area was either controlled across numerosities (Experiments 1, 2 and 4) or increased congruently with numerosity (Experiment 3). There was no evidence of a SNARC effect either across the full range, or within the subset of the subitizing range. The results of Experiment 4 (in which we presented the original stimuli of Mitchell et al.) suggested that visual properties of non-symbolic displays can prompt SNARC-like effects driven by visual cues rather than numerosity. Taken in the context of other recent findings, we argue that non-symbolic representations of number do not offer a direct and automatic route to numerical-spatial associations.

The Use of Bruner’s Modes of Representations in Teaching Factoring Second-Degree Polynomials

2012 ◽  
Vol 1 (1) ◽  
Author(s):  
Jerr A. Cabahug
Keyword(s):  
Conceptual Understanding ◽  
Teaching Mathematics ◽  
Abstract Concepts ◽  
Symbolic Representations ◽  
Teaching Aids ◽  
The Common ◽  
Common Problems ◽  
Factoring Polynomials ◽  
Iconic Representations ◽  
Second Degree

In teaching mathematics, one of the common problems of teachers is how to teach unfamiliar and abstract concepts in such a way that the students would make sense of them. One of these ways is the use of the different teaching aids which are reflected in Bruner’s Theory. In his theory, Bruner argued that conceptual understanding could be enhanced if students are exposed to different representations of a concept. In particular, he identified three main types of representations: concrete, iconic, and symbolic. Bruner’s theory stipulates that all three modes can be utilized in introducing abstract concepts for students. Based on this theory, this paper discusses one possible set of activities in teaching the topic of factoring second-degree polynomials. In this set of activities, the students will be taught first to factor polynomials using algebraic tiles which constitutes concrete representation of the concept; followed by factoring polynomials using pictures as iconic representations; and lastly, the students will be taught on how to factor polynomials using algebraic patterns which are the symbolic representations.   Keywords - Bruner’s Theory; representations; teaching; factoring second-degree polynomials; conceptual understanding

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