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Sizes, ratios, approximations: On what and how the ANS represents.
1Faculty of Philosophy, New College of the Humanities at Northeastern, LondonWC1B 3HH, UK. brian.ball@nchlondon.ac.uk; brianandrewball.wordpress.com.
The Behavioral and Brain Sciences
|December 15, 2021
Summary
The approximate number system (ANS) likely represents ratios, not rational numbers, challenging existing theories. This suggests a distinction between representing magnitudes and intensities in numerical cognition.
Area of Science:
- Cognitive Science
- Numerical Cognition
- Psychology
Background:
- The approximate number system (ANS) is crucial for numerical cognition.
- Previous research proposed the ANS represents rational numbers.
Purpose of the Study:
- To evaluate the claim that the ANS represents rational numbers.
- To clarify whether the ANS represents magnitudes or intensities.
Main Methods:
- Analysis of evidence presented in Clarke and Beck's proposal.
- Theoretical examination of number representation in cognitive systems.
Main Results:
- Evidence supports the ANS representing ratios and positive integers, not general rational numbers.
- Rational numbers function as extensive magnitudes, while ratios act as intensities.
Conclusions:
- The ANS likely represents ratios (intensities), not rational numbers (magnitudes).
- The distinction between WHAT a system represents and HOW it represents is critical and interdependent.
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