Catalog: KH0134 (UR1120, AS120)

Section Information
Statistics:
Aliases:   UR1120, AS120
Contributors:  Marcia & Robert Ascher
Museum:  Museum für Völkerkunde (Ethnologische Museum), Berlin, Germany
Museum Number:  VA47083
Provenance:  Ica
Region:  Unknown 		# of Groups & Cords:   4 Groups, 36 Cords - (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 (KH0154)  Next (KH0159)
   KH0134 (UR1120, AS120)
Indexed Pendant Sum
Colored Pendant Sum
DataFile:
KH0134
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 KH00110.
  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 KH0134 (UR1120, AS120):

Year Author Title Pages
2009 Artzi, Bat-Ami. The secret of the knot: khipu No. 936 from the Maiman collection. Masters thesis, Hebrew University. Text: 53-54
1978 Ascher, Marcia, and Robert Ascher. Code of the Quipu: Databook. University Microfilms, Ann Arbor. Text: 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. Text: 89; 144,146-7 (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. Text: 282
2010 Chirinos Rivera, Andrés. Quipus del Tahuantinsuyo: Curacas, Incas y su saber matemático en el siglo XVI. Editorial Commentarios, Lima. Text: 210-213; 233-235; 238; 276; 278-285; 340; Figures: 278; 281; 282; 356
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. Text: 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. Figures: fig.1.3 (p.9)
2020 Medelius Olcese de Riveros, Y.M., 2021. Dando cuentas: los quipucamayos en las comunidades indígenas y ante la administración colonial. Perú, siglo XVI. Doctoral Thesis. Universidad Pablo de Olavide de Sevill. Olcese de Riveros, Y.M., 2021. Dando cuentas: los quipucamayos en las comunidades indígenas y ante la administración colonial. Perú, siglo XVI. Doctoral Thesis. Universidad Pablo de Olavide de Sevilla Text: 122
2021 Medrano, Manuel. Knot Just Numbers: Mathematics and More in Andean Khipu Strings. Manuscript. Text: 6
2022 Medrano, M.A. The promise of Andean khipu transcriptions: a multi-scale investigation (Doctoral dissertation, University of St Andrews). Text: 89
1996 Pereyra S., Hugo. Acerca de dos quipus con características numéricas excepcionales. Bulletin de l’Institut francais d’études Andins 25(2):203-231. Text: 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. Figures: fig.2 (p.99)
2025 Salas Garcia, José Antonio. La Interpretación Lingüística de los Quipus. Ernst & Young, Lima, Peru. Text: 209; Figures: 208
2022 Setlak, Magdelena Anna. Hacia una lexicografía de los quipus: estudio etnohistórico sobre la función y contenido del sistema andino de registros de la información mediante cuerdas y nudos. Doctoral Thesis. Universidad Complutense de Madrid. Figures: fig.7 (p.32, 650)
2024 Thompson, Karen M. A Numerical Connection Between Two Khipus. Ñawpa Pacha, pp.1-22. Text: 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. Text: 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 Figures: fig.1.6 (p.8)
2007 Urton, Gary. The Khipus from Laguna de los Cóndores. Nuevas Imágenes S.A., Lima. Figures: fig.6 (p.14)
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. Figures: fig.1.2.3 (p.36)
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. Figures: fig.13.11 (p.333)
2012 Urton, Gary. Mathematics and Accounting in the Andes before and after the Spanish Conquest. In Alternative forms of knowing (in) mathematics: Celebrations of diversity of mathematical practices (pp. 17-32). Rotterdam: SensePublishers. Figures: fig.1.2 (p.20)
2014 Urton, Gary. Quipus de Pachamac. Ministerio de Cultura, Lima. Figures: fig.17 (p.25)
2017 Urton, Gary. Inka History in Knots: Reading Khipus as Primary Sources. University of Texas Press, Austin. Text: 261; Figures: fig.2.4 (p.48)
2019 Urton, Gary. Algunas reflexiones sobre la escritura de la historia del Tahuantinsuyo a partir de fuentes primarias (quipus). Allpanchis 46(83):13-38. Figures: fig.4 (p.20)
2007 Witkowski, Olaf. Essai de décryptage des cordelettes quipus utilisées par les Incas comme moyen de communication: Un exemple d’ethno-cryptographie (Doctoral dissertation, Master’s thesis, Université Catholique de Louvain). Text: 87, 97