Tawa Pukllay Proof: new method for solving arithmetic operations with the Inca Yupana using pattern recognition and parallelism

Abstract

Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Yupana Inka Tawa Pukllay (YITP), where arithmetic operations do not require mental calculations: no carries, no borrows, no memorization of multiplication tables, nor trial and error procedures for divisions. Instead, user recognizes patterns and makes predefined movements to perform the four basic arithmetic operations very quickly; moreover, the result of the operation can be reached by multiple paths and in parallel, allowing each user to create his own strategies. This article rigorously demonstrates that YITP produces correct numerical results as a basis for the generation of new electronic devices in computing.