Methodological reflections on typologies for numerical notations (Q2894215)

The present paper provides a classification scheme or typologies for 100 distinct systems of notations for representing natural numbers. A general framework for assessing the efficacy of these typologies relative to certain desiderata is presented. This framework is used to discuss the two influential typologies of Zhang \& Norman and Chrisomalis. A new typology is presented that takes as its starting point the principles by which numerical notations represent multipliers and bases. It has been shown by different examples that this new typology provides a more refined classification of numerical notations than the ones put forward previously. Many of the world's numerical notations and their analysis in terms of typology discussed in the present paper are presented in the Appendix.