The Inca Philosophy of 10

Abstract

In his Gramática y arte nueva de la lengua general o lengua del Inca, Gonçalez Holguín ([1607] 1842:217) describes the unique Quechua arithmetical system and presents the names of the numbers in Quechua in a decisively decimal outline, beginning in ‘1’ and finishing in the ‘infinite’—that is, a list of positive integers (Z+) that does not include ‘zero.’ In his list, each numeral in Quechua appears with its translation into Spanish and a representation in western Indo-Arabic numerals. However, even though the systems would be seemingly identical (i.e., decimal), the representation of Quechua numerals in Western ones reveals, in fact, an essential cultural discrepancy, as the graphic representations of the Western numerals, from 0 to 9, and their combinations used to construct numbers higher than 10, did not exist in Inca culture, and their decimal system, as will be shown below, was based on utterly different concepts, structures and visualization means. Among these concepts, the ‘count by 10’ and powers of ten, building on other basic concepts (such as hanan-hurin, for example), turns out to be an inherent element of Inca thought applied by these to structure and manage the Tawantinsuyu’s[1] territory and society.   [1]     Tawantinsuyu is the original Inca name of the so-called ‘Inca Empire.’