In Andean society, numbers served not only a quantitative but also a qualitative purpose, and the mathematical nature of quipus corresponded to what Galen Brokaw has called “a numerical episteme.” Andean society was characterized by a high degree of numerical literacy and organized its social and philosophical thought according to an episteme rooted in numbers. The number ten was key in this epistemology, and social groups or villages (called ayllus) were organized according to the decimal unit of ten. Guaman Poma’s survey of Inca society corresponds to this decimal organization, with its ten “calles.” In addition to the decimal-based system of social organization, the number five organized both historical and geographical paradigms in the Andes, as evident in the separation of Cuzco into four parts organized around a “fifth” part, the center. The pair constituted another important numerical unit. A preference for pairs reflected the philosophical notion that singularity signified incompletion and also dangerous imbalance. Pairs represented balance and a completed unit. This philosophy, based on the concept of pairing and the privileging of dualism, pervaded Andean society and thought. Arithmetic, whether addition, subtraction, multiplication, or division, was central to the “art of rectification” by which Andean society sought to maintain balance and equilibrium in moral and social terms. Numbers and their arithmetical manipulation then provides “a process by which indigenous Andean culture shapes the raw, quantitative nature of time, space, and social organization into numerically significant contributions” based on its “ontology of numbers.”
In Andean epistemology, numbers can therefore be understood as parallel to words as the privileged signifiers through which reality was understood, represented, and manipulated. Like other kinds of writing, quipus then reflected the privileged forms of representation in Andean society. Indeed, Brokaw has argued that “the Andean ontology of numbers and the conventions of khipu textuality developed together dialogically, even informing and influencing the other.” The Aschers coined the term “cultural insistence” to explain the ways in which the main ideas, values, and organizational structures of a given culture manifest themselves in material and representational artifacts. They note that cloth was such an important component of Inca culture that it can be seen as “characteristic of Inca insistence in and of itself. At every turning point in the life history of an individual cloth played a key role.” The Aschers argue that portability was equally characteristic of Inca “insistence” and that the most common artifact used to carry things was a piece of strong cloth. The quipu, then, appears to have combined numerous central elements of Andean cultural insistence as a cloth-based, highly portable system of literacy based on an epistemology of numbers.