Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism

Dhavit Prem; Rosario Guzman-Jimenez; Fernando Sotomayor; Alvaro Saldivar

doi:10.1109/FAIML57028.2022.00048

Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism

Dhavit Prem
, Rosario Guzman-Jimenez
, Fernando Sotomayor
, Alvaro Saldivar

Research output: Chapter in Book/Report/Conference proceeding › Paper (Conference contribution) › peer-review

2 Scopus citations

Abstract

Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Tawa Pukllay (TP), 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 paper proves with mathematical rigor that TP produces correct numerical results.

Original language	English
Title of host publication	Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	209-218
Number of pages	10
ISBN (Electronic)	9781665473644
DOIs	https://doi.org/10.1109/FAIML57028.2022.00048
State	Published - 2022
Event	2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022 - Virtual, Online, China Duration: 19 Jul 2022 → 21 Jul 2022

Publication series

Name	Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022

Conference

Conference	2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022
Country/Territory	China
City	Virtual, Online
Period	19/07/22 → 21/07/22

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10.1109/FAIML57028.2022.00048

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Prem, D., Guzman-Jimenez, R., Sotomayor, F., & Saldivar, A. (2022). Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism. In Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022 (pp. 209-218). (Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FAIML57028.2022.00048

Prem, Dhavit ; Guzman-Jimenez, Rosario ; Sotomayor, Fernando et al. / Tawa Pukllay Proof : New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism. Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022. Institute of Electrical and Electronics Engineers Inc., 2022. pp. 209-218 (Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022).

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title = "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: Tawa Pukllay (TP), 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 paper proves with mathematical rigor that TP produces correct numerical results.",

author = "Dhavit Prem and Rosario Guzman-Jimenez and Fernando Sotomayor and Alvaro Saldivar",

note = "Publisher Copyright: {\textcopyright} 2022 IEEE.; 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022 ; Conference date: 19-07-2022 Through 21-07-2022",

year = "2022",

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series = "Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022",

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Prem, D, Guzman-Jimenez, R, Sotomayor, F & Saldivar, A 2022, Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism. in Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022. Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022, Institute of Electrical and Electronics Engineers Inc., pp. 209-218, 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022, Virtual, Online, China, 19/07/22. https://doi.org/10.1109/FAIML57028.2022.00048

Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism. / Prem, Dhavit; Guzman-Jimenez, Rosario; Sotomayor, Fernando et al.
Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 209-218 (Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022).

Research output: Chapter in Book/Report/Conference proceeding › Paper (Conference contribution) › peer-review

TY - GEN

T1 - Tawa Pukllay Proof

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AU - Prem, Dhavit

AU - Guzman-Jimenez, Rosario

AU - Sotomayor, Fernando

AU - Saldivar, Alvaro

PY - 2022

Y1 - 2022

N2 - Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Tawa Pukllay (TP), 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 paper proves with mathematical rigor that TP produces correct numerical results.

AB - Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Tawa Pukllay (TP), 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 paper proves with mathematical rigor that TP produces correct numerical results.

UR - https://www.scopus.com/pages/publications/85144622486

U2 - 10.1109/FAIML57028.2022.00048

DO - 10.1109/FAIML57028.2022.00048

M3 - Articulo (Contribución a conferencia)

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BT - Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022

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ER -

Prem D, Guzman-Jimenez R, Sotomayor F, Saldivar A. Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism. In Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022. Institute of Electrical and Electronics Engineers Inc. 2022. p. 209-218. (Proceedings - 2022 International Conference on Frontiers of Artificial Intelligence and Machine Learning, FAIML 2022). doi: 10.1109/FAIML57028.2022.00048

Tawa Pukllay Proof: New Method for Solving Arithmetic Operations with The Inca Yupana Using Pattern Recognition and Parallelism

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