See the facsimile on the Guaman Poma Website of the Royal Library of Denmark.
http://www.kb.dk/permalink/2006/poma/info/en/frontpage.htm
[comments available in english and spanish]
The original manuscript was digitalized around the year 2000, in true colors (various shades of black to brown ink). [ so ... the colorful reproductions that we see here and there on the internet are not taken from the original manuscript ]
Each of the ~1200 pages, including 398 full-page drawings, can be examined closely, and downloaded, as a fine definition image. (click on the button "Larger Image")
The website also links to a wealth of digital resources related to Guaman Poma and his time.
We can read [http://wayback-01.kb.dk/wayback/20101105080508/http://www2.kb.dk/elib/mss/poma/docs/adorno/2002/index.htm] that before 2000, the manuscript already had a "history" (that is not considered to have excessively reduced its readibility) :
Yupana - hints to Andrés Chirinos Rivera's theory
I had already found a short explanation, by Chirinos himself, in two videos on Ytb channel "walter gonzales arnao" in spanish : http://youtu.be/zzA9hKfw-tQ and http://youtu.be/tBZRofCHts8 (and now - july 20, 2014 - I find http://youtu.be/y7MCaqMFGc0 , which didn't seem understandable to me).
But there is something more complete : see page 32 of the user manual for the TK-Yupana tool (Tk-Yupana r07, by Kunturweb) : http://kunturweb.altervista.org/tk-yupana/doc/tk-yupana-EN.pdf.
The document describes various known theories about the Yupana. Around page 32, begins the description of Chirinos' theory. How to perform calculations with Chirinos' system is not yet described in this version of the document.
Use :
- the board is used in the vertical position
- each row represents a power of ten, from 0 (bottom) to n-1 (n=number of rows)
- each circle in each row of the board represents a different value (from 1 to 11) from right to left
- seeds are placed in the circles only [ 0 or 1 seed in each circle, probably ]
Value of each circle in a row is as follows :
extract from: Table 14: Chirinos' Yupana scheme
Comments
At first glance the system doesn't seem of the most practical kind :
But there is something more complete : see page 32 of the user manual for the TK-Yupana tool (Tk-Yupana r07, by Kunturweb) : http://kunturweb.altervista.org/tk-yupana/doc/tk-yupana-EN.pdf.
[ this version is no longer available as of July 21 2014, but the Spanish and Italian versions are still there : http://kunturweb.altervista.org/tk-yupana/doc/tk-yupana-ES.pdf and http://kunturweb.altervista.org/tk-yupana/doc/tk-yupana-IT.pdf ; and the english version is also on http://es.sourceforge.jp/projects/sfnet_tk-yupana/downloads/doc/tk-yupana-EN.pdf/ ]
Use :
- the board is used in the vertical position
- each row represents a power of ten, from 0 (bottom) to n-1 (n=number of rows)
- each circle in each row of the board represents a different value (from 1 to 11) from right to left
- seeds are placed in the circles only [ 0 or 1 seed in each circle, probably ]
Value of each circle in a row is as follows :
Comments
At first glance the system doesn't seem of the most practical kind :
- requires a very precise placing of seeds,
- multiplies the opportunities of mistakes : from mispositioning, from movements of the board, and because there is no intuitive hints to the value of each circle in a cell, it is difficult [at least for slightly dyslexic people] to remember the value of each circle, ...
- actually, this last point is not so important - see below some easily memorized configurations - when you memorize the configurations of simple numbers, you don't really need to memorize the value of the cells (sort of).
- collaborative calculus is less easy (several people seated around a board, each with a differing view of it, will have more difficulty - than with various other systems - to know the value of the seeds),
- requires a rather carefully crafted board : using an improvised earthy or sandy surface as a board is almost impossible,
- performing a multiplication with one board only and without knowing the tables doesn't seem allowed easily.
[ update 2014-03-10 : I tried with a big multiplication : rather interesting http://youtu.be/m3n6QhZslLc
]
Guáman Poma’s Yupana and Inca Astronomy, Subhash Kak
"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. [...]
Pre-Columbian dice in the Andean region
Using a Yupana with dice, in Inca times ?
Was the Yupana sequence (1,2,3,5) also present in Inca dice ?
Using a Yupana with a few dice, instead of seeds, is much easier.
Less manipulations are required, as each face of a dice represents a group of seeds.
So, I searched the internet, to verify if this unusual way of doing was feasible in Inca times :
Dice were often pyramidal in the Andean region :
4 sided and 6 sided,
http://boardgamestudies.info/pdf/issue1/BGS1Depaulis.pdf
http://ex.ludicum.org/publicacoes/bgsj/1
Inca Dice and Board Games / Thierry Depaulis, Board Games studies, 1998
4 sided, in this order : 2, 3, 1, 4
With dice, its easier to perform big multiplications with a Yupana, without knowing the multiplication tables.
See a simple way to do that, here :
So, I searched the internet, to verify if this unusual way of doing was feasible in Inca times :
- what kind of dice did they have ?
- were they numbered in the sequence 1,2,3,5 that is used in the Yupanas ?
Dice were often pyramidal in the Andean region :
- 4 sided (square base) truncated pyramids, numbered 1,2,3,4.
- five or six-sided truncated pyramids.
- related to games named by the number 5 (depending of the language and depending of the transcription : huayro, pichca, wayru, pichqa, pichka, pisca, pichica, pichiqa, huayru, huairu, wayru, guayro, ...).
Details ...
4 sided and 6 sided,
http://ex.ludicum.org/publicacoes/bgsj/1
Inca Dice and Board Games / Thierry Depaulis, Board Games studies, 1998
- 2 illustrations (extracted from a publication dated 1918) representing dice found in the Museo de Chile ; numbering is not entirely visible ; drawings page 45
- 1 illustration of a "modern" dice, six sides, pyramidal, sequence 1,0,4,2,5,3 [ same as below, where it is said to have been found in use in the '60 (1960) ] ; drawing, page 30
4 sided, in this order : 2, 3, 1, 4
Fire-making apparatus in the US National Museum - Walter Hough - 1890
Hough, Walter. Fire-Making Apparatus in the IT. S. National Museum, An. Rep. U. S. Nat. Mus.,
1888, pp. 531-587.
https://archive.org/details/firemakingappara00houguoft
The former publication has a revision and extension
"No. 2735.—Proceedings U. S. National Museum, Vol. 73, Art. 14."
http://si-pddr.si.edu/dspace/bitstream/10088/15753/1/USNMP-73_2735_1928.pdf
Quick comparison : 17 more (useful) pages in the extended publication
1888, pp. 531-587.
https://archive.org/details/firemakingappara00houguoft
you can also download it in pdf format
The former publication has a revision and extension
"No. 2735.—Proceedings U. S. National Museum, Vol. 73, Art. 14."
FIRE-MAKING APPARATUS IN THE UNITED STATES
NATIONAL MUSEUM By Walter Houghhttp://si-pddr.si.edu/dspace/bitstream/10088/15753/1/USNMP-73_2735_1928.pdf
Quick comparison : 17 more (useful) pages in the extended publication
Une étude du réglage de bâtons de jet et de boomerangs traditionnels
"Une étude du réglage de bâtons de jet et de boomerangs traditionnels"
A study of traditionnal throwing sticks and boomerang tuning
"A study of traditionnal throwing sticks and boomerang tuning", BORDES Luc, Bulletin of Primitive Technology, fall 2011:N°42
Use of Blogger as a repository of shared links ?
Wanted a space to easily store/search/find/edit/share links to papers of interest.
Also needed to be able to redirect people to one of those links, as part of an answer to questions asked on my Youtube channel.
Creating and maintaining web pages or documents is costly. Posting in G+ seems to result in a real chaos. Youtube's descriptions and posts are useful for... scattering information and forget about it. Gmail could be only a personal repository.
So, I'm testing Blogger and GGroups, but may revert to the simple use of the discussion section of my youtube channel.
Also needed to be able to redirect people to one of those links, as part of an answer to questions asked on my Youtube channel.
Creating and maintaining web pages or documents is costly. Posting in G+ seems to result in a real chaos. Youtube's descriptions and posts are useful for... scattering information and forget about it. Gmail could be only a personal repository.
So, I'm testing Blogger and GGroups, but may revert to the simple use of the discussion section of my youtube channel.
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