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. With dice, its easier to perform big multiplications with a Yupana, without knowing the multiplication tables.
So, I searched the internet to verify if this unusual way of doing was at least 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 ?
Answer, in short :
No mention of the sequence 1,2,3,5 in dice.
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, ...).
4 sided and 6 sided,
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
“La Pichca”: Recuperando el patrimonio intangible de los Pueblos Originarios de América”. Stela Maris Ferrarese Capettini. Museo del Juguete Étnico “Allel Kuzen”
A dice found in the Haichol cave (see drawings below, from other articles) is said to be of the same type as dice used in the Inca empire. The numbers on the 4 sides are in this order : 2, 3, 1, 4; the base has no number.
4 sided (square base) truncated pyramid (1,2,3,4) :
Dos "Pirámides" de Caspana, El juego de la Pichica y el dominio Inka en el loa superior [northern Chile].
3 dice of the same kind (pyramid ; 1, 2, 3, 4) :
- one found in the Mapuche zone, citation attributed to R. Lenz,
- one found in a Museum of Natural History (where ? Chile ?), citation attributed to L. Matus,
- one found in the Mapuche territory (search "Varinia Varela" to wich it is attributed)
Several (truncated) pyramidal dice :
- 2 dice found in "Huaca Tres Palos", Rimac valley [Peru, Lima, Maranga], drawing of the dice : end of page 88 [one "1,2,3,4" , the other "1,3,2,4"]
- 1 dice found in Pachacamac, Lurin valley [Peru, Lima], see drawing ; beginning of page 89 (order : 1,3,2,4)
- several dice found in Machu Pichu, Urubamba valley [Peru] and said to have been made by a pre-inca megalithic people [like peoples from Chavin or Tiahaunacu] ; 3 dice are described :
- one resembling the Huaca Tres Palos one,
- another is a truncated pyramid with incides lines,
- the third is a rectangular parallelepiped (see drawing, beginning of page 90 ; order : 1 or 5 ?, 2, 3, 4)
- 1 dice found in Casabindo, Jujuy [Northern Argentina], truncated pyramid (1,3,2,4), see drawing page 91
- 1 dice found in Viluco, Mendoza province [Argentina] : square based pyramid, with dots, order 1,3,3,4 (no face with a 2), drawing page 95
- 1 dice found in Chenque Haichol, Neuquen province [Argentina] : square based pyramid, with dots, order 1,2,3,4 ; drawing page 96
- another drawing, page 3 of
- Several bone dice found in the Sierra del Ecuador : hegagonal base, six sided pyramids, 1 of them is in the sequence 1,0,2,3,4,5 another one is in the sequence 1,0,4,2,5,3 ; drawings page 99
(c - dice found in use around 1965 : not pre-colombian )
Other beautiful images found on the facebook page of the
museo nacional de historia natural de-chile
(also here : http://www.mnhn.cl/613/w3-article-73666.html)
Not any other andean dice ?
see them all (low quality photos, but with maps showing where they were found) here :