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

Abstract

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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.

Keywords

• Analog Number System
• number comparison
• Weber's law
• diffusion model
• symbolic numbers