scholarly journals The Source of the Symbolic Numerical Distance and Size Effects

2016 ◽  
Author(s):  
Attila Krajcsi ◽  
Gábor Lengyel ◽  
Petia Kojouharova
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Mathematical Knowledge ◽  
Semantic Network ◽  
Number System ◽  
Numerical Distance ◽  
Alternative Account ◽  
Semantic System ◽  
Alternative Approach ◽  
Conceptual Network

Human number understanding is thought to rely on the analogue number system (ANS), working according to Weber’s law. We propose an alternative account, suggesting that symbolic mathematical knowledge is based on a discrete semantic system (DSS), a representation that stores values in a semantic network, similar to the mental lexicon or to a conceptual network. Here, focusing on the phenomena of numerical distance and size effects in comparison tasks, first we discuss how a DSS model could explain these numerical effects. Second, we demonstrate that DSS model can give quantitatively as appropriate a description of the effects as the ANS model. Finally, we show that symbolic numerical size effect is mainly influenced by the frequency of the symbols, and not by the ratios of their values. This last result suggests that numerical distance and size effects cannot be caused by the ANS, while the DSS model might be the alternative approach that can explain the frequency-based size effect.

scholarly journals Professional mathematicians do not differ from others in the symbolic numerical distance and size effects

2020 ◽  
Author(s):  
Mateusz Hohol ◽  
Klaus Willmes ◽  
Edward Nęcka ◽  
Bartosz Brożek ◽  
Hans-Christoph Nuerk ◽  
...  
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Reference Group ◽  
Distance Effect ◽  
Numerical Distance ◽  
Single Digit ◽  
Mathematical Skills ◽  
Numerical Distance Effect ◽  
Individual Level ◽  
The Individual

The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes.

scholarly journals Symbolic number comparison is not processed by the analogue number system: different symbolic and nonsymbolic numerical distance and size effects

2017 ◽  
Author(s):  
Attila Krajcsi ◽  
Gabor Lengyel ◽  
Petia Kojouharova
Keyword(s):  
Size Effects ◽  
Goodness Of Fit ◽  
Numerical Cognition ◽  
Reaction Times ◽  
Number System ◽  
Error Rates ◽  
Numerical Distance ◽  
Comparison Task ◽  
Number Comparison ◽  
Symbolic Number

Dominant numerical cognition models suppose that both symbolic and nonsymbolic numbers are processed by the Analogue Number System (ANS) working according to Weber’s law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and nonsymbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times and diffusion model drift rates were systematically analyzed in both nonsymbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model’s prediction is relatively good for the nonsymbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only nonsymbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.

scholarly journals Non-numerical Distance and Size Effects in an Ant

2020 ◽  
Vol 11 (2) ◽  
pp. 13
Author(s):  
Marie-Claire Cammaerts ◽  
Roger Cammaerts
Keyword(s):  
Size Effect ◽  
Operant Conditioning ◽  
Size Effects ◽  
Visual Cues ◽  
Distance Effect ◽  
Just Noticeable Difference ◽  
Numerical Distance ◽  
Weber's Law ◽  
Different Dimensions ◽  
Similar Elements

The distance effect (the fact that the individuals’ discrimination between two similar elements increases with the magnitude of the distance between them) as well as the size effect (the fact that the individuals’ discrimination between two similar elements decreases with the size of these elements) have been largely reported in vertebrates but not in invertebrates. Here, we demonstrate their existence in an ant, using operant conditioning to visual cues (black circles) of different dimensions. The two effects were obvious and differed from one another. Both effects could be accounted for Weber’s law, but it was here not tempted to verify if they are in line with this law by defining the just noticeable difference the ants can perceive between the cues.

scholarly journals Processing symbolic numbers: The example of distance and size effects

2020 ◽  
Author(s):  
Attila Krajcsi ◽  
Petia Kojouharova ◽  
Gabor Lengyel
Keyword(s):  
Size Effects ◽  
Alternative Model ◽  
Numerical Cognition ◽  
Number System ◽  
Approximate Number System ◽  
Comparison Task ◽  
Semantic System ◽  
Simple Representation

According to the dominant view in the literature, several numerical cognition phenomena are explained coherently and parsimoniously by the Approximate Number System (ANS) model, which model supposes an evolutionarily old, simple representation behind many numerical tasks. We offer an alternative model, the Discrete Semantic System (DSS) to explain the same phenomena in symbolic numerical tasks. Our alternative model supposes that symbolic numbers are stored in a network of nodes, similar to conceptual or linguistic networks. The benefit of the DSS model is demonstrated through the example of distance and size effects of comparison task.

Origins of the Sample-Size Effect in Explicit Evaluative Judgment

2009 ◽  
Vol 56 (5) ◽  
pp. 344-353 ◽  
Author(s):  
Martina Kaufmann ◽  
Tilmann Betsch
Keyword(s):  
Size Effect ◽  
Sample Size ◽  
Information Integration ◽  
Size Effects ◽  
Target Object ◽  
Attitude Formation ◽  
Evaluative Judgment ◽  
Alternative Account ◽  
Sample Size Effect ◽  
Implicit And Explicit

This research considers situations in which individuals explicitly form attitude judgments toward a target object after considering a sample of information. Previous research shows sample-size effects under such conditions: Increasing sample size can produce more extreme judgments. Commonly, these effects are attributed to summative processes in information integration. Alternatively, this research proposes that sample size affects perceived reliability of information, which in turn affects the extremity of the subsequent judgment. Three experiments were conducted to empirically substantiate this alternative account. Experiment 1 provides evidence that participants perceive larger samples as more reliable than smaller samples. Experiment 2 demonstrates that perceived reliability mediates the sample-size effect on judgments. Experiment 3 shows that other variables, such as variability, which lowers the perceived reliability, attenuate sample-size effects. The results are explained with reference to the value account model of attitude formation, stating that implicit and explicit modes of attitude formation are guided by different principles of information integration.

Particle size effects in the selective hydrogenation of cinnamaldehyde over supported palladium catalysts

RSC Advances ◽  
2016 ◽  
Vol 6 (79) ◽  
pp. 75541-75551 ◽  
Author(s):  
Feng Jiang ◽  
Jian Cai ◽  
Bing Liu ◽  
Yuebing Xu ◽  
Xiaohao Liu
Keyword(s):  
Particle Size ◽  
Size Effect ◽  
Selective Hydrogenation ◽  
Size Effects ◽  
Palladium Catalysts ◽  
Particle Size Effect ◽  
Particle Size Effects ◽  
Supported Palladium Catalysts ◽  
Supported Palladium ◽  
Palladium Particles

Palladium particles of different sizes obtained directly and indirectly by various methods were studied to clarify the particle size effect in the selective hydrogenation of cinnamaldehyde (CAL).

Modeling of Size Effects on the Flow Stress of Type 304 Stainless Steel and Application in Coining Process

2007 ◽  
Author(s):  
Gap-Yong Kim ◽  
Muammer Koc ◽  
Jun Ni
Keyword(s):  
Grain Size ◽  
Stainless Steel ◽  
Flow Stress ◽  
Size Effect ◽  
Size Effects ◽  
Specimen Size ◽  
304 Stainless Steel ◽  
Length Scales ◽  
Type 304 ◽  
Type 304 Stainless Steel

Application of microforming in various research areas has received much attention due to the increased demand for miniature metallic parts that require mass production. For the accurate analysis and design of microforming process, proper modeling of material behavior at the micro/meso-scale is necessary by considering the size effects. Two size effects are known to exist in metallic materials. One is the “grain size” effect, and the other is the “feature/specimen size” effect. This study investigated the “feature/specimen size” effect and introduced a scaling model which combined both feature/specimen and grain size effects. Predicted size effects were compared with experiments obtained from previous research and showed a very good agreement. The model was also applied to forming of micro-features by coining. A flow stress model for Type 304 stainless steel taking into consideration the effect of the grain and feature size was developed and implemented into a finite element simulation tool for an accurate numerical analysis. The scaling model offered a simple way to model the size effect down to length scales of a couple of grains and extended the use of continuum plasticity theories to micro/meso-length scales.

Study of the Size Effects and Friction Conditions in Microextrusion—Part II: Size Effect in Dynamic Friction for Brass-Steel Pairs

2007 ◽  
Vol 129 (4) ◽  
pp. 677-689 ◽  
Author(s):  
Lapo F. Mori ◽  
Neil Krishnan ◽  
Jian Cao ◽  
Horacio D. Espinosa
Keyword(s):  
Grain Size ◽  
Friction Coefficient ◽  
Size Effect ◽  
Contact Pressure ◽  
Size Effects ◽  
Numerical Models ◽  
Kolsky Bar ◽  
Experimental Results ◽  
Material Response ◽  
Dynamic Coefficients

In this paper, the results of experiments conducted to investigate the friction coefficient existing at a brass-steel interface are presented. The research discussed here is the second of a two-part study on the size effects in friction conditions that exist during microextrusion. In the regime of dimensions of the order of a few hundred microns, these size effects tend to play a significant role in affecting the characteristics of microforming processes. Experimental results presented in the previous companion paper have already shown that the friction conditions obtained from comparisons of experimental results and numerical models show a size effect related to the overall dimensions of the extruded part, assuming material response is homogeneous. Another interesting observation was made when extrusion experiments were performed to produce submillimeter sized pins. It was noted that pins fabricated from large grain-size material (211μm) showed a tendency to curve, whereas those fabricated from billets having a small grain size (32μm), did not show this tendency. In order to further investigate these phenomena, it was necessary to segregate the individual influences of material response and interfacial behavior on the microextrusion process, and therefore, a series of frictional experiments was conducted using a stored-energy Kolsky bar. The advantage of the Kolsky bar method is that it provides a direct measurement of the existing interfacial conditions and does not depend on material deformation behavior like other methods to measure friction. The method also provides both static and dynamic coefficients of friction, and these values could prove relevant for microextrusion tests performed at high strain rates. Tests were conducted using brass samples of a small grain size (32μm) and a large grain size (211μm) at low contact pressure (22MPa) and high contact pressure (250MPa) to see whether there was any change in the friction conditions due to these parameters. Another parameter that was varied was the area of contact. Static and dynamic coefficients of friction are reported for all the cases. The main conclusion of these experiments was that the friction coefficient did not show any significant dependence on the material grain size, interface pressure, or area of contact.

scholarly journals Size Effect in Fracture of Sandwich Structure Components: Foam and Laminate

2001 ◽  
Author(s):  
Zdeněk P. Bažant ◽  
Yong Zhou ◽  
Drahomír Novák ◽  
Isaac M. Daniel
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Sandwich Structure ◽  
Maximum Load ◽  
Material Strength ◽  
Large Structures ◽  
Nominal Strength ◽  
Sandwich Plates And Shells ◽  
Extensive Test ◽  
Plates And Shells

Abstract In the design of sandwich plates and shells for very large structures, such as ships in the range of 100 m length, it is very important to take the size effect on the nominal strength into account, and do so in a realistic, physically justified, manner. Before the size effect is addressed for a sandwich structure, it must be understood for its components — the foam core and the laminate skins. In the current practice, the size effects are automatically attributed to the randomness of material strength, as described by the Weibull theory. The purpose of this paper is to show that in both the foam and the laminate there are deterministic size effects, which are generally more pronounced. They are caused by stress redistribution and energy release due to the growth of large fractures or large cracking zones prior to attaining the maximum load. This deterministic size effect is verified and calibrated by new tests of notched specimens of rigid close-cell vinyl foam. A combined deterministic-probabilistic theory of size effect of the laminates is proposed and verified by extensive test data.

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