The Inka Khipu and Yupana : A Reply to Zen Vasconcellos and Rojas Gamarra (2026)

Abstract

ABSTRACT A new analysis by Zen Vasconcellos and Rojas Gamarra offers a novel interpretation of the Inka devices used for calculating ( yupana ) and recording ( khipu ) numbers. They claim the Inka devices represented numbers neither positionally , with place value, as most researchers have assumed, nor additively , without place value, a possibility uniquely explored by Florio. Instead, Z&R claim the yupana worked positionally in calculating, while the khipu represented calculation inputs and outputs additively, a hybrid configuration. The new work also substantially comments on Florio and Overmann's materially based interpretation of the Inka devices. As the authors of the 2025 article, we analyze the proposed hybrid model, Florio from the perspective of mathematical logic and Overmann from historical and cross‐cultural number systems. We conclude the proposed hybrid model is unrealistic.