Updating the Abstract-Concrete Distinction in Ancient Near Eastern Numbers: Notes

*    J. Cale Johnson, Dwight Read, Rex Welshon, Robert K. Englund, Steven Chrisomalis, and an anonymous reviewer offered many helpful comments on the initial draft; any remaining errors and omissions are, of course, my own.


1    Piaget envisioned the child’s acquisition of number as a process of developing “biologically predetermined” cognitive structures through environmental interaction; Damerow argued that environmental interaction (particularly with material representations of number) could influence the substance of numerical content (Damerow 1998: 128). With Material Engagement Theory, material structures become a constitutive component of numerical cognition.


2    This is not an argument for retaining the term “abstract,” but rather, a stipulation that “independence” is another aspect of the quality to which “abstract” has historically been applied.


3    The idea that fingers (and possibly toes) were an early material form for Mesopotamian counting is inferred from extant number systems, where the strong somatic basis for numbers manifests as patterning by fives, tens, and twenties. This somatic basis is a function of the neurological interaction between the intraparietal sulcus (the part of the brain implicated in appreciating quantity; e.g., Ardila 2010) and the angular gyrus (the part that “knows” the fingers and supports both finger-counting and calculating; e.g., Roux et al. 2003). Finger-counting spans the gamut of numerical elaboration (i.e., from emerging to highly elaborated systems), while the use of body parts other than the fingers (e.g., toes; other anatomical features) is associated with emerging number systems (especially ones that have not incorporated other material forms). Mesopotamian numbers would have shared these cross-cultural tendencies, as Ancient Near Eastern people are reasonably and plausibly construed to have had five-fingered hands and typical neurological functionality (and indeed, the latter is supported by linguistic evidence). A more detailed discussion is outside the present scope but is planned.