UR1120/KH0134 - Catalog Information

Section Information
Statistics:
Original Name:   AS120
Original Author:  Marcia & Robert Ascher
Museum:  Museum fĂĽr Völkerkunde,
Museum Number:  VA47083
Provenance:  Ica
Region:  Unknown 		# of Cords:   36 (32p, 4s)
# of Unique Cord Colors:  10
Benford Match:  0.9573
# Ascher Sums (pps, ips, cps, sps,...):  12 (0, 7, 5, 0,...)
Similar Khipu:  Previous (UR1180)  Next (UR1143)
   UR1120/KH0134
Indexed Pendant Sum
Colored Pendant Sum
DataFile:
UR1120
Notes:
Ascher Databook Notes:
  1. This is one of several khipus acquired by the Museum in 1907 with provenance Ica. For a list of them, see UR1100.
  2. By spacing, the khipu is separated into 4 groups of 8 pendants each. The color pattern for each group is the same (with the minor exception that pendants 7 and 8 in group 4 are B:GG and B/B-GG rather than the B-GG and B/B:GG of similar positions). In each group, there is one subsidiary on position 3 and it is the color of the pendant to which it is attached.
  3. The values in group 1 are the sums of the values of groups 2-4, position by position (with a discrepancy of 1 in the 4th position). The value on the subsidiary on position 3 in group 1 is also the sum of the values of the subsidiaries on position 3 in groups 2-4. Thus:
    \[ \sum\limits_{i=2}^4 P_{ij} = P_{1j}\;\;\;\;\;for\;\;j=(1,2,...,8) \]
  4. The ratios of the corresponding values is surprisingly consistent. For j =2,..., 8 and the position 3 subsidiary value:

    p2j/P1j = 0.342 max. deviation 1.2%
    p3j/P1j = 0.425 max. deviation 0.7%
    p4j/P1j = 0.235 max. deviation 0.9%

    The values on the exceptional position ( i=1) in the different groups, counterbalance each other. If 796 were subtracted from position 1 in group 3 and added to position 1 in group 4, the values in position 1 would also satisfy the above ratios.
Bibliography:

Bibliography for UR1120/KH0134:

Year Author Title Pages
2009 Artzi, Bat-Ami. The secret of the knot: khipu No. 936 from the Maiman collection. Masters thesis, Hebrew University. 53-54
1978 Ascher, Marcia, and Robert Ascher. Code of the Quipu: Databook. University Microfilms, Ann Arbor. 698; 796-799
1981 Ascher, Marcia, and Robert Ascher. Code of the Quipu: A Study in Media, Mathematics, and Culture. University of Michigan Press, Ann Arbor. 89; 144-145, 146 (ex.7.5)
1986 Ascher, Marcia. Mathematical Ideas of the Incas.’ In Native American Mathematics, edited by Michael P. Closs, pp. 261–289. University of Texas Press, Austin. 282
2010 Chirinos Rivera, Andrés. Quipus del Tahuantinsuyo: Curacas, Incas y su saber matemático en el siglo XVI. Editorial Commentarios, Lima. 210-213; 233-235; 238; 276; 278-285; 289; 292; 340
1996 Christensen, Antje. The Peruvian quipu. In History and science of knots, edited by J. C. Turner and P. van de Griend, pp. 71-88. World Scientific, New Jersey. 82, 83-84
2019 Clindaniel, Jon. Toward a Grammar of the Inka Khipu: Investigating the Production of Non-numerical Signs. PhD dissertation, Graduate School of Arts & Sciences, Harvard University. -
2021 Medrano, Manuel. Knot Just Numbers: Mathematics and More in Andean Khipu Strings. Manuscript. 6
1996 Pereyra S., Hugo. Acerca de dos quipus con características numéricas excepcionales. Bulletin de l’Institut francais d’études Andins 25(2):203-231. 188-202
2014 Saez-Rodriguez, Alberto. Khipu UR19: Inca Measurements of the Moon’s Diameterand its Distance from the Earth. Revista Latinoamericana de Etnomatemática: Perspectivas Socioculturales de la Educación Matemática 7(1):96–125. 99
2024 Thompson, Karen M. A Numerical Connection Between Two Khipus. Ă‘awpa Pacha, pp.1-22. 20
1994 Urton, Gary. New Twist in an Old Yarn: Variation in Knot Directionality in the Inka Khipus. Baessler-Archiv Neue Folge 42:271-305. 298
2003 Urton, Gary. Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records. University of Texas Press, Austin. http://www.jstor.org/stable/10.7560/785397 -
2007 Urton, Gary. The Khipus from Laguna de los Cóndores. Nuevas Imágenes S.A., Lima. -
2008 Urton, Gary. Mathematics and authority: a case study in Old and New World accounting. In The Oxford Handbook of the History of Mathematics, edited by Eleanor Robson and Jacqueline Stedall, pp.27-56. Oxford University Press, New York. -
2011 Urton, Gary, and Carrie J. Brezine. Khipu Typologies. In Their Way of Writing: Scripts, Signs, and Pictographies in Pre-Columbian America, edited by Elizabeth Hill Boone and Gary Urton, pp. 319–352. Dumbarton Oaks Research Library and Collection, Washington. -
2014 Urton, Gary. Quipus de Pachamac. Ministerio de Cultura, Lima. -
2017 Urton, Gary. Inka History in Knots: Reading Khipus as Primary Sources. University of Texas Press, Austin. 261
2019 Urton, Gary. Algunas reflexiones sobre la escritura de la historia del Tahuantinsuyo a partir de fuentes primarias (quipus). Allpanchis 46(83):13-38. -