Project

An alternative model for symbolic number processing

Goal: Symbolic and non-symbolic numbers are thought to be processed by an evolutionary ancient, simple representation, the Analogue Number System (ANS), which system is thought to be the very base of number understanding.

We offer an alternative account for symbolic number understanding, proposing a human specific, simple representation similar to a network of concepts or to the mental lexicon. It is a comprehensive model for symbolic number processing phenomena.

See more details at http://www.thenumberworks.org/discrete_semantic_system.html

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Project log

Attila Krajcsi
added an update
Approximate Number System and Discrete Semantic System have different predictions about the relationship of comparison and priming distance effects. We found no correlation between the effects. Another reason to doubt that ANS supports simple symbolic number processing. https://doi.org/10.3758/s13423-022-02108-x
 
Attila Krajcsi
added an update
We summarize our former findings why symbolic number comparison cannot be a psychophysical process and why it cannot be backed by the Approximate Number System.
 
Attila Krajcsi
added an update
In a new work we demonstrated that the size effect of Indo-Arabic number comparison is influenced by the frequency of the numbers in that session. This finding extends our former work where we revealed that size effect in artificial, new symbols comparison task, the size effect depends entirely on the frequency of the symbols ( ). Now we have also shown that session statistics also influences the Indo-Arabic size effect, although the size effect changes only partially. See more details in https://doi.org/10.1016/j.actpsy.2018.11.009 .
 
Attila Krajcsi
added an update
In our recent work we have demonstrated that Indo-Arabic numerical distance effect is an association effect between the digits and the small-large categories, and it does not depend on the ratio of the numbers. In other words, symbolic numerical distance effect is not the consequence of the Weber’s law. This result again questions whether the Approximate Number System model can be relevant in symbolic number processing, and how individual differences in distance effect can be interpreted. Find our paper at https://doi.org/10.1007/s00426-018-1052-1 More details about our project is at http://www.thenumberworks.org/discrete_semantic_system.html.
 
Attila Krajcsi
added an update
A new numerical interference, the PNARC (parity-number) effect is described in our recently published paper. The interference with the parity is important, because parity is a discrete property, and it raises the question whether numerical interferences are rooted in an analog number representation. Not surprisingly, we think that this new result is in line with our Discrete Semantic System model.
Additionally, we introduced a new method to reveal interferences where the direction of the interference is not uniform in the sample, and in which case the usual calculation method couldn't find the effect.
 
Attila Krajcsi
added an update
There has been quite a few former works demonstrating that both symbolic and nonsymbolic number comparison can be best described with the psychophysics model that is also utilized in physical feature comparison tasks. We took a more detailed look, and found that although symbolic number comparison is quite similar to that supposed performance, still, there are critical differing features, suggesting that it is not the Approximate Number System that supports symbolic number comparison. Find our paper at https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00124/ .
 
Attila Krajcsi
added an update
Do you use number comparison distance effect to measure the basis of numerical abilities? In our newly published paper we demonstrate that the symbolic numerical distance effect does not rely on the Approximate Number System (e.g., the distance effect cannot be used to measure the Weber fraction), but it is an association effect (association between the numbers and the large-small categories). See our paper at https://doi.org/10.3389/fpsyg.2017.02013. More information at https://sites.google.com/site/mathematicalcognition/home/discrete-semantic-system.
 
Attila Krajcsi
added an update
Yet another analysis showing that symbolic number comparison effects are not rooted in the Analogue Number System. Beyond the usual goodness of fit, we investigated several properties of how ANS model describes symbolic and nonsymbolic number comparison performance. We consistently found that while the ANS model describes the nonsymbolic number comparison quite precisely, symbolic number comparison works differently. (We know, some people say that it’s trivial to find that symbolic and nonsymbolic comparisons work differently, but while saying this they forget that the whole ANS fuss is about the similar mechanism behind symbolic and nonsymbolic number processing.) See our preprint at https://psyarxiv.com/dmau5/. As always, any feedback is welcome.
 
Attila Krajcsi
added an update
Another evidence showing that symbolic number comparison is not supported by the Analogue Number System. In a number comparison task we manipulated the associations between the numbers and the larger category, and the distance effect followed this manipulated statistical property, but not the ratio of the numbers. See our preprint at https://psyarxiv.com/bpy9c/ . Any feedback is welcome.
 
Attila Krajcsi
added an update
Our second paper about our alternative model for symbolic number processing is out. It describes our models in more details, and demonstrates that this model can be used to explain symbolic numerical phenomena known in the literature.
Critically, it also shows that the size effect (more difficult processing of large numbers than small numbers in number comparison) is not the result of the ratio of the number, but it is a frequency effect: Larger numbers are less frequent, that is why they are more difficult to process. This frequency based size effect phenomenon seriously challenges the Approximate Number System account.
 
Attila Krajcsi
added an update
Our first paper about our alternative model for symbolic number processing is out. The work demonstrates that numerical comparison and size effects are independent effects in symbolic Indo-Arabic numbers, and not the consequences of a single ratio effect. Find it on the Psychonomic Bulletin & Review website (http://link.springer.com/article/10.3758/s13423-016-1175-6) or on our project web page (https://sites.google.com/site/mathematicalcognition/home/discrete-semantic-system#TOC-Numerical-distance-and-size-effects-are-independent-in-symbolic-comparison-task).
 
Attila Krajcsi
added a project goal
Symbolic and non-symbolic numbers are thought to be processed by an evolutionary ancient, simple representation, the Analogue Number System (ANS), which system is thought to be the very base of number understanding.
We offer an alternative account for symbolic number understanding, proposing a human specific, simple representation similar to a network of concepts or to the mental lexicon. It is a comprehensive model for symbolic number processing phenomena.