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The abacus representation of numeral systems
1Department of Philosophy, McGill University, Montreal, Quebec, Canada.
Summary
This study presents a new abacus-based framework to systematically represent numeral systems, including irregular ones. This model allows for abstract comparisons across diverse formats like written or verbal numbers.
Area of Science:
- Cognitive Science
- Mathematics
- Linguistics
Background:
- Numeral systems exhibit diverse structures and irregularities.
- Existing frameworks may not adequately capture the internal logic of all systems.
- Cross-cultural and cross-format comparisons of numeration are challenging.
Purpose of the Study:
- To introduce a novel theoretical framework for representing the internal structure of numeral systems.
- To provide a systematic method for describing diverse numeral systems, including irregular ones.
- To enable structural comparisons of numeral systems across different representational formats.
Main Methods:
- Development of an abacus-based theoretical framework.
- Utilizing labels and reading conventions for abacus entries and columns.
- Application of the framework to decimal place-value and Roman numeral systems as examples.
Main Results:
- The abacus framework systematically represents numeral systems, accommodating sub-bases and irregularities.
- It distinguishes between systems like decimal (equal column heights) and Roman (variable column heights).
- The framework's abstract nature facilitates structural comparisons across notational, verbal, and body-based formats.
Conclusions:
- The proposed abacus representation offers a uniform and abstract method for analyzing numeral system structures.
- This framework supports the systematic study and comparison of diverse numeration systems.
- It provides a basis for discussing irregularities and commonalities in how humans represent numbers.
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