Letters

Inka Accounting Practices

Science  23 Dec 2005:
Vol. 310, Issue 5756, pp. 1903-1904
DOI: 10.1126/science.310.5756.1903d

We are delighted that G. Urton and C. J. Brezine have discovered concrete examples of khipus indicating the existence of an accounting hierarchy similar to those previously postulated (“Khipu accounting in ancient Peru,” Reports, 12 Aug., p. 1065). Nevertheless, we would like to amplify various points raised by their Report.

We were surprised that the authors recounted the theory of the Inka administration's decimal structure without mentioning works that express serious doubts about the concrete application of this kind of administration at the regional level (14). It appears that the system was rarely exact even when a decimal vocabulary was used (57). The population of the Inka province of Huayla, for example, consisted of 12 guaranga (the Quechua term for a group of 1000), which were split into 4 units of 3 guaranga. Yet, on the eve of Spanish conquest, two of the guaranga in a known unit had approximately 750 taxpayers and one had 950 (5).

Urton's and Brezine's discovery of identical khipus accords well with previous accounts of exact copies of khipus shown to Spanish administrators and judges in the 16th century (8, 9). Nevertheless, Spanish transcriptions and translations of khipus do not support Urton and Brezine's hypothesis that the khipu system was flexible, tolerating inexact counts and matches. Colonial testimonies argue unanimously for the exactitude of the system (10).

We have demonstrated previously that when khipus were read, every now and then ±1 errors occurred on whichever decimal level (10). Nevertheless, we consider it unlikely that almost half of the summation numbers would have been encoded erroneously, as proposed for khipu UR068. There may be various explanations other than that of Urton and Brezine for the closeness of the summation numbers. In early colonial khipus, this kind of variation can be found, for example, in the annual fulfillment of earlier taxation requirements known as the Spanish tasa (10).

Finally, Urton and Brezine argue that the khipus of the upper hierarchy include place identifiers. Indeed, toponyms and personal names have previously been treated as part of khipu texts (2, 11). We also have argued that the main towns of the Inka State had specific numeric values that were encoded in khipus, and furthermore, that more complicated systems seem to have been used to encode the names of minor villages and the many personal names that appear in various decoded khipu texts in Spanish historical records (5, 10). To us, it seems that Urton and Brezine have applied our hypothesis to their specific case. Unfortunately, they do not manage to prove anything and the statement continues to be an unproven hypothesis.

References and Notes

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Response

Pärssinen and Kiviharju's comments and references point out a number of important issues we were unable to cover in our Report because of space constraints.

It is our understanding that both precise decimal administration and variations on this concept existed in the Inka empire. Colonial informants, especially those in the former capital Cusco (14), presented decimal administration as a complete, ideal system, although it is clear that the reality in the provinces was quite different from that ideal. Pärssinen and Kiviharju question the inaccuracy of the Puruchuco khipu; it is our belief that such inaccuracy is precisely the sort of variance from ideal decimal values that may have characterized Inka decimal administration at the provincial or local level. The principal task in interpreting pre-Hispanic and colonial record keeping in the Andes remains one of attempting to understand the causes and the significance of differences between colonial informants' testimony about Inka administration in comparison to the information actually recorded (often from khipu transcriptions) in colonial censuses and other statistical records. While we were not surprised that the decimal ideal was not reflected in the numbers and sums recorded in the Puruchuco khipu, we still believe that describing the ideal is essential to gaining a full picture of Inka administrative practices.

Although much of the material discussed in our Report is based on analysis of numerical values on the khipu, we were led to that analysis through other structural similarities within this group of artifacts: pendant cord spacing, color repetitions, and relative position of numerical magnitudes within their pendant groups. Therefore, our hypothesis of an accounting hierarchy is not based solely on the numbers, which indeed do not represent exact summations between levels I and II.

We regret that we did not specifically mention work on the referencing of toponyms and personal names in the khipu (5, 6), and we appreciate the inclusion of additional references in their Letter.

Finally, we take this opportunity to remind readers that complete data on all of the khipu discussed in our Report are available on our Web site, http://khipukamayuq.fas.harvard.edu/.

References and Notes

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