AS038/KH0049

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Khipu Notes Exist - See Below

 Original Name: AS038
Original Author: Marcia & Robert Ascher
Museum: Museo Nacional de Arqueología, Antropología e Historia de Perú
Museum Number: MNAAHP3550
Provenance: Unknown
Region: Costa Sur 		Total Number of Cords: 367
Number of Ascher Cord Colors: 12
Benford Match: 0.968
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Datafile: KH0049

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Khipu Notes

Ascher Databook Notes:
  1. The khipu was repaired and sewn to a cloth backing in 1974 by Company Estela. Since the pendant fragments that were added to broken pendants on the main cord are not part of the original construction, we have considered the fragments as broken and then listed the fragments separately. Several other fragments associated with the khipu are also listed. Our subsequent analysis lead to conclusions about the probable placement of these fragments.
  2. The Museum designates the khipu as part of the Collection Museo Historia 1928.
  3. By spacing, there are 6 groups of 18 pendants each. Within each group, the same basic color pattern is repeated: 2W, 2 mixed, 5W, 2B, 2 mixed, 5B.
    For group 1, the mixed colors are B: BD for the first pair and B for the next pair. In groups 2-6, the mixed colors are BD: W for all pairs.
    1. There are no subsidiaries on the pendants in group 1. Group 4 has subsidiaries only on pendants in positions 1,3,10 and 12. Groups 2-5 have 0-6 subsidiaries in positions 2-9 and 11-18 but 6-9 subsidiaries in positions 1 and 10.
    2. By color, there are 11 subsidiary categories. None of the pendants have all of them.
      In general, they appear in the same color order even though there are only some of the colors present.
      (The order is: RL: GG, B:W, B, BD:W, W, B, W, GG, RL, BD, BS.) BD: W appears only on positions 14 and 15 in group 5 and RL: GG, RL and BD appear only on positions 1 and 10.
  5. Each group of 18 pendants can be considered as 2 subgroups of 9 consecutive pendants each since
    1. the basic color pattern of the pendants and presence or absence of subsidiaries in positions 1-9 is repeated for positions 10-18, and
    2. the order of magnitude of the values of pendants 1 and 10 and their subsidiaries is larger than the others.
  6. Groups 1 and 2 are sumgroups of groups 3-6.
    1. For the first 12 positions, values in group 2 are the sums of values in the corresponding positions in groups 4, 5, 6.
      Then for one position, one value is not included and so the next 5 sums involve values in 2 corresponding positions and one neighboring position. That is:
      \[P_{2i}=P_{4i}+P_{5i}+P_{6i}\;for\;i=(1,2,3...,12) \]
      \[P_{2,13}=P_{5,13}+P_{6,13} \]
      \[P_{2,i}=P_{4,i-1}+P_{5i}+P_{6i}\;for\;i=(14,15,...,18) \]
    2. Values in group 1 are the sums of values in corresponding positions in groups 2 and 3:
      \[P_{1i}=P_{2i}+P_{3i}\;for\;i=(1,2,3...,18) \]
      Since group 2 sums groups 4, 5, 6, these could alternately be interpreted as the sums of values in groups 3, 4, 5, 6.
    3. Subsidiaries on pendants in group 2 sum the subsidiaries, color by color, on the corresponding pendants in groups 3, 4, 5, 6.
      Subsidiaries with color RL: GG, B:W, and BD:W are not summed. Thus:
      \[P_{2,i°sub_j}=P_{3,i°sub_j}+P_{4,i°sub_j}+P_{5,i°sub_j}+P_{6,i°sub_j}\;for\;i=(1,2,3...,18)\;\;\;j=(B,W,B,W,GG,RL,BD,BS) \]
    4. It is interesting to observe that the pendants in group 1 have the sums of pendant values in groups 3-6, while it is in group 2 that the subsidiaries have the sums of the subsidiary values in groups 3-6.
      Also, when describing the pendant value sums, the values in group 4 were offset for positions 14-18. Since there are no subsidiaries on these pendants, we can reach no conclusion as to whether offsetting was necessary in the representation of the subsidiary sums also.
  7. There are some discrepancies in the summations described in observation 6.
    1. Whether due to our difficulty in counting knots and assigning colors since the khipu was sewn to a cloth, or due to khipu maker inaccuracies, there are a number of sums off by 1 in 1 digit. The 36 pendant sums involved about 500 individual digits so 7 single digit discrepancies are not considered significant. Similarly, there are about 256 subsidiaries with 500 digits involved in the 70 or so subsidiary sums. Fourteen discrepancies of differences of 1 in single digits or misassociated colors is, again, more than usual but not significant.
    2. The discrepancies in the summations that are noteworthy occur in positions 1 and 10. They are important because they corroborate that these positions are analogous (i. e., the first pendant in each of the subgroups constituting a group) and anomalous (i. e., different in order of magnitude and number of subsidiaries). The sums on pendants 1 in groups 1 and 2 are off by 3 in 27,000 and 15,000 respectively, while the sums on pendants 10 in groups 1 and 2 are off by more, but are still less than 4% off. The sums on 6 of the 8 subsidiaries on pendant 1 in group 2 are exact but 2 are not and on pendant 10 in group 2, the same 2 colors (and 1 more) are inexact while 5 of the 8 are exact. Hence, these positions are still viewed as conforming to the general summation pattern although they represent something else as well.