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Against a century of inclusive studies, this book presents a new interpretation of the Inca calculating board known as the yupana, based on a different set of assumptions. Instead of seeing Inca numbers as positional, like the modern Hindu-Arabic numerals used by Western researchers, this new approach looks at them as additive, similar in organization to the numbers of ancient civilizations like Egypt. By analyzing Guamán Poma's work and considering the nature of the materials used by the Inca for recording and calculating with numbers, this new work finds a mathematical message, a multiplication algorithm, in the historical drawing. Finding a multiplication in the ancient drawing leads to considering the decipherment correct. The text is written to be accessible to non-experts, as well as experts in fields other than mathematics. The work is addressed to researchers in the field, those interested in the history of mathematics, those attracted by mathematical enigmas, and especially the Andean peoples searching for lost knowledge of their past.
List of contents
1 Introduction.- 2 Quipus recounted in the Chronicles and the studies to decipher them.- 3 Additive and positional numerical systems.- 4 Do quipus represent an additive or positional number system?.- 5 The yupana.- 6 Chronological list of studies of Guamán Poma s yupana.- 7 Differences between deciphering a linguistic message and a mathematical one.- 8 Translating Guamán Poma s yupana as a multiplication.- 9 The implications of detecting a multiplication in Guamán Poma s yupana.- 10 Preconceptions preventing the yupana from being identified as a multiplication.- 11 Potential arithmetical operations on Guamán Poma s yupana.- Appendices A: Probability of randomly inserted counters.
Summary
Against a century of inclusive studies, this book presents a new interpretation of the Inca calculating board known as the yupana, based on a different set of assumptions. Instead of seeing Inca numbers as positional, like the modern Hindu-Arabic numerals used by Western researchers, this new approach looks at them as additive, similar in organization to the numbers of ancient civilizations like Egypt. By analyzing Guamán Poma's work and considering the nature of the materials used by the Inca for recording and calculating with numbers, this new work finds a mathematical message, a multiplication algorithm, in the historical drawing. Finding a multiplication in the ancient drawing leads to considering the decipherment correct. The text is written to be accessible to non-experts, as well as experts in fields other than mathematics. The work is addressed to researchers in the field, those interested in the history of mathematics, those attracted by mathematical enigmas, and especially the Andean peoples searching for lost knowledge of their past.
