Counting Systems

Data allow the identification of several stages in the evolution of counting systems. The pre‐numerical token system as found in the Near East – containing symbols that convey quantity and commodity in one form – prepared the ground for numeracy in some languages. Certain aspects of the token system are found in measurement systems as well, where each commodity has its own linguistic units of quantification and conversion factors. While these systems were very early, they linger in numerous languages today, even those that feature full‐fledged decimal numerals. Numerical systems are based on numerals and are sequential, but they may vary substantially, also reflecting here different stages of development. Concrete numerals, for example, continue the link between quantity and commodity found in measurement and token systems. Body‐part numerals may have relatively high upper limits, but they need additional linguistic specification or gestures (multimodality) to convey precise information. Moreover, early abstract numeral systems in general have no or low bases and relatively low upper limits; they tend to be monomorphemic and to exclusively favor addition in compounds. Later systems by contrast typically are characterized by abstract and decimal numerals, (often combined) arithmetical operations, recursion, high upper limits (‘infinite’), and consistency. Because of this consistency at all levels – base, operations, recursion – the modern decimal system has a low level of complexity in comparison to early counting systems.