*"Guáman Poma’s Yupana and Inca Astronomy", Subhash Kak, Oklahoma State University, Stillwater, OK 74078, USA*[no date, uploaded in 2014 on arXiv.org, last updated 17 Feb 2014]

Paper : http://arxiv.org/ftp/arxiv/papers/1401/1401.7637.pdf

Abstract : http://arxiv.org/abs/1401.7637

Conclusions :

**[...] the yupana of Guáman Poma most likely served the purpose of**

**counting days for calendric use**. [...]

See page 1 and page 2 for a quick refutation of previous theories (from Wassen's one to de Pasquale or Florio's ones) as arbitrary, leading to no advantage in calculations, not intuitively reasonable, .... Cruel, but, I'm afraid, funny to read when you tend to agree :-)

- Note that the author does not mention A. Chirinos Rivera's theory (2010).
- C.Florio's open answer to Kak's refutation is here : Risposta aperta a Subhash Kak sulla yupana di Guaman Poma de Ayala (in italian). We read that Kak's theory is substantially identical
*[?]*to de Pasquale's theory, only more complex*[using base 144 instead of base 40]*. There is also a verbal explanation about Florio's theory. The paper ends with a cruel and persuasive critique about Kak's calendrical interpretation of meaningless numbers.*[one hypothesis could have been suggested : that calendrical interpretation may simply be a humorous parody, a mischievous hoax :-) ].*

See page 5, chapter "IV. BASIC FUNCTION GPY", for an interpretation of the Yupana working in base 144. This follows (page 4) a mathematical description of the structure of an abacus with sub-bases, if one was needed.

Some comments

The date of the paper is unknown, but according to the bibliography section, it seems not to be earlier than 2010 [november 2010 : publication date for a paper from Leonard Molly and alt. in J. of Math. and Culture] and maybe not much later (as A. Chirinos Rivera's book was published in sept. 2010 and is not mentionned). Not sure that I can boast of beeing the first to "publish" [ on YTB :-) ] something related to Yupana and base 144... But at least, in my first vids, the numbers shown on Guáman Poma's drawing are, like in the paper, 92, 31, 29, 79, and 56.

One can wonder whether the use of the Yupana from left to right and bottom to top, would be the only one to give birth to the hypothesis of the calendric use. As in the paper, that hypothesis derives from the presence of the numbers 6, 24, 72, 92, 31, 29, 79, and 56.

For instance, the use of the Yupana from right to left, bottom to top, as an abacus in base 144, shows sub-bases 2, 6, 24. The numbers shown on Poma's drawing, with such a way of using the Yupana, would be 67, 32, 122, 31, 58.

(not from the paper)

Those numbers are different from the previous set of numbers, except for 6, 24, 31.

- Can we find a calendric meaning to this new set of numbers ?
- Or, if we can't, should we conclude that theYupana was not used from right to left as a base 144 abacus ?

:-)

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