The source of the symbolic numerical distance and size effects

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 the 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

Visual mismatch negativity and stimulus-specific adaptation: the role of stimulus complexity

The present study investigated the function of the brain activity underlying the visual mismatch negativity (vMMN) event-related potential (ERP) component. Snowflake patterns (complex stimuli) were presented as deviants and oblique bar patterns (simple stimuli) as standards, and vice versa in a passive oddball paradigm. Control (equiprobable) sequences of either complex shape patterns or oblique bar patterns with various orientations were also presented. VMMN appeared as the difference between the ERP to the oddball deviant and the ERP to the control (deviant minus control ERP difference). Apart from the shorter latency of the vMMN to the oblique bar pattern as deviant, vMMN to both deviants was similar, i.e., there was no amplitude difference. We attributed the function of the brain processes underlying vMMN to the detection of the infrequent stimulus type (also represented in memory) instead of a call for further processing (a possibility for acquiring more precise representation) of the deviant. An unexpected larger adaptation (control minus standard ERP difference) to the snowflake pattern was also obtained. We suggest that this was due to the acquisition of a more elaborate memory representation of the more complex stimulus

Symbolic Numerical Distance Effect Does Not Reflect the Difference between Numbers

In a comparison task, the larger the distance between the two numbers to be compared, the better the performance—a phenomenon termed as the numerical distance effect. According to the dominant explanation, the distance effect is rooted in a noisy representation, and performance is proportional to the size of the overlap between the noisy representations of the two values. According to alternative explanations, the distance effect may be rooted in the association between the numbers and the small-large categories, and performance is better when the numbers show relatively high differences in their strength of association with the small-large properties. In everyday number use, the value of the numbers and the association between the numbers and the small-large categories strongly correlate; thus, the two explanations have the same predictions for the distance effect. To dissociate the two potential sources of the distance effect, in the present study, participants learned new artificial number digits only for the values between 1 and 3, and between 7 and 9, thus, leaving out the numbers between 4 and 6. It was found that the omitted number range (the distance between 3 and 7) was considered in the distance effect as 1, and not as 4, suggesting that the distance effect does not follow the values of the numbers predicted by the dominant explanation, but it follows the small-large property association predicted by the alternative explanations

Mechanisms of spatial contextual cueing in younger and older adults

The contextual cueing effect is the phenomenon observed when response time (RT) becomes faster in visual search in repeated context compared with a new one. In the present study we explored whether the mechanisms involved in the effect are age dependent. We investigated it in younger (N=20, 12 women, 21.2±1.75 years) and older (N=19, 9 women, 67.05±3.94 years) adults. We found a faster target identification in the repeated configurations with similar magnitude in the two age-groups, which indicates that this contextual cueing effect remained intact even in the older participants. To shed light on the underlying mechanisms, we measured and compared the amplitude of three event-related potentials: N2pc, P3, and response-locked LRP. In the younger group, the larger contextual cueing effect (novel-minus-repeated RT difference) correlated positively with a larger difference in amplitude for repeated compared to novel configurations for both the N2pc and the P3 components; but there was no correlation with the rLRP amplitude difference. However, in the older group, only the rLRP amplitude difference between novel and repeated configurations showed an enhancement with larger contextual cueing. These results suggest that different mechanisms are responsible for the contextual effect in the two age-groups. It has both an early and an intermediate locus in younger adults: effective attentional allocation and successful stimulus categorization, or decision-making confidence are involved; while in older adults, a late locus was identified: a more efficient response organization led to a faster reaction

Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects

HIGHLIGHTSWe test whether symbolic number comparison is handled by an analog noisy system.Analog system model has systematic biases in describing symbolic number comparison.This suggests that symbolic and non-symbolic numbers are processed by different systems.Dominant numerical cognition models suppose that both symbolic and non-symbolic numbers are processed by the Analog 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 non-symbolic 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 non-symbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model's prediction is relatively good for the non-symbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation

Symbolic numerical distance effect does not follow the values of the numbers

In a comparison task, the larger the distance between the two numbers to be compared, the better the performance, a phenomenon termed the numerical distance effect. According to the dominant explanation, the distance effect is rooted in a noisy representation, and performance is proportional to the size of the overlap between the noisy representations of the two values. According to alternative explanations, the distance effect may be rooted in the association between the numbers and the small-large categories, and performance is better when the numbers show relatively high differences in their strength of association with the small-large properties. In everyday number use the value of the numbers and the association between the numbers and the small-large categories strongly correlate, thus, the two explanations have the same predictions for the distance effect. To dissociate the two potential sources of the distance effect, in the present study participants learned new artificial number digits between 1 and 3, and between 7 and 9, thus, leaving out the numbers between 4 and 6. It was found that the omitted number range (the distance between 3 and 7) was considered in the distance effect as 1, and not as 4, suggesting that the distance effect does not follow the values of the numbers predicted by the dominant explanation, but it follows the small-large property association predicted by the alternative explanations