title: The Role of Number Notation: Sign-Value Notation Number Processing is Easier than Place-Value.
abstract: Number notations can influence the way numbers are handled in computations; however, the role of notation itself in mental processing has not been examined directly. From a mathematical point of view, it is believed that place-value number notation systems, such as the Indo-Arabic numbers, are superior to sign-value systems, such as the Roman numbers. However, sign-value notation might have sufficient efficiency; for example, sign-value notations were common in flourishing cultures, such as in ancient Egypt. Herein we compared artificial sign-value and place-value notations in simple numerical tasks. We found that, contrary to the dominant view, sign-value notation can be applied more easily than place-value notation for multi-power comparison and addition tasks. Our results are consistent with the popularity of sign-value notations that prevailed for centuries. To explain the notation effect, we propose a natural multi-power number representation based on the numerical representation of objects.
authors.affiliation: Department of Radiology, Harvard Medical School, Brigham and Women's Hospital Boston, MA, USA ; Department of Cognitive Psychology, Eötvös Loránd University Budapest, Hungary.
authors.forename: Attila
authors.initials: A
authors.lastname: Krajcsi
authors.forename: Eszter
authors.initials: E
authors.lastname: Szabó