UR1175/KH0192 - Catalog Information

Section Information
Statistics:
Original Name:   AS175
Original Author:  Marcia & Robert Ascher
Museum:  Museum für Völkerkunde,
Museum Number:  VA42518
Provenance:  Pachacamac
Region:  Unknown 		# of Cords:   338 (224p, 114s)
# of Unique Cord Colors:  10
Benford Match:  0.84
# Ascher Sums (pps, ips, cps, sps,...):  239 (103, 51, 48, 34,...)
Similar Khipu:  Previous (UR1152)  Next (UR1126)
   UR1175/KH0192
Pendant Pendant Sum
Indexed Pendant Sum
Colored Pendant Sum
Subsidiary Pendant Sum
Group Group Sum
Ascher Decreasing Group
DataFile:
UR1175
Notes:
Ascher Databook Notes:
  1. This is one of several khipus acquired by the Museum in 1907 with provenance Pachacamac. For a list of them, see UR1097.
  2. By spacing, the khipu is separated into 45 groups of 5 pendants each. There is a larger space after every 3rd group and a still larger space between the 21st and 22nd groups and the 24th and 25th groups. Thus, the khipu is in 3 parts: part 1 is 7 sets of 3 groups each; part 2 is 1 set of 3 groups; and part 3 is 7 sets of 3 groups.
  3. All groups in part 1 have the same color pattern: W (with a W subsidiary); LB (with an LB subsidiary); YG; YB; YB: 0G. Groups in parts 2 and 3 have the same pattern for the first 3 pendant positions and then vary in one or both of the last 2 positions. Calling the colors in the part 1 pattern C1-C5, the color patterns are summarized in Table 1.

    TABLE 1

    Part 1 (groups 1-21)C1C2C3C4C5
    Part 2 (groups 1-3)C1C2C3C4C4
    Part 3 (groups 1-5)C1C2C3C2C5
    Part 3 (groups 6-8)C1C2C3C2C4
    Part 3 (groups 9-21)C1C2C3C4C4


    In all groups, there is at least one subsidiary on pendants 1 and 2 (a W and an LB respectively) and no subsidiaries on the other positions. Additional subsidiaries on the first 2 positions are, with one exception, KB:W or LB-W.
  4. In parts 1 and 3, many values are repeated in the same position in consecutive groups or in the same position 2 groups later. The former can be represented as:,

    Pij= Pi+1,j and the latter as Pij = Pi+2,j

    In part 1, these hold in 20 and 12 places respectively; in part 2 in no places; and in part 3 in 27 and 18 places.

  5. The values in part 2 are related to the sums of values in part 3. Position by position, values in group 1 of part 2 are related to the sums of values in the first groups in each of the 7 sets in part 3; group 2 values are related to sums of values in the second groups of each of the sets; and group 3 values to the sums of values of the third group. That is:
    \[ P_{2ij}= \sum\limits_{k=0}^{6} P_{3,3k+i,j}\;\;\;for\;j=(1,2,...5),\;\; i=(1,2,3) \]
    This represents 15 sums and 105 values being summed. Of the 15 values in part 2, 8 are exactly these sums (or off by 1 in 1 digit); 5 are exact sums of only some of the 7 pendants:

    Example: P211 = P341 + P3,10,1 + P3,13,1 + P3,16,1 + P3,19,1 thus omitting P311 and P371

    and 2 are less than the sums but cannot be associated with a specific subset of the 7 pendants. (Note that the main cord is broken and so there could have been another part prior to part 1 that summed its values.
Bibliography:

Bibliography for UR1175/KH0192:

Year Author Title Pages
1978 Ascher, Marcia, and Robert Ascher. Code of the Quipu: Databook. University Microfilms, Ann Arbor. 1057-1074
1981 Ascher, Marcia, and Robert Ascher. Code of the Quipu: A Study in Media, Mathematics, and Culture. University of Michigan Press, Ann Arbor. 86; 91; 93 (ex.5.4)
1983 Ascher, Marcia. The Logical-Numerical System of Inca Quipus. Annals of the History of Computing 5:268–278. DOI: 10.1109/MAHC.1983.10090 275
2005 Ascher, Marcia. How Can Spin, Ply, and Knot Direction Contribute to Understanding the Quipu Code? Latin American Antiquity 16(1):99–111. 101; 108-109; 110
2006 Pereyra Sánchez, Hugo. Descripción de los quipus del Museo de Sitio de Pachacamac. Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica, Lima. 14
1994 Urton, Gary. New Twist in an Old Yarn: Variation in Knot Directionality in the Inka Khipus. Baessler-Archiv Neue Folge 42:271-305. 287; 297
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 -
2014 Urton, Gary. Quipus de Pachamac. Ministerio de Cultura, Lima. 44
2017 Urton, Gary. Inka History in Knots: Reading Khipus as Primary Sources. University of Texas Press, Austin. 123; 261