Abstract
This article analyzes the potential khipu-document “match” involving six Inka-style khipus from Peru’s Santa Valley that record data similar to a 1670 colonial census of San Pedro de Corongo. Despite its potential as a breakthrough in khipu decipherment, crucial details surrounding these potential “Rosetta khipus” and their associated colonial document have been left out, overlooked, or confused in the literature. This article’s objective is to synthesize and evaluate what is known about this khipu-document “match” while also using combinatorics to identify an optimal moiety alignment for the six lineage groups listed in the 1670 census. This novel moiety alignment differs from the one proposed in 2018 by Manuel Medrano and Gary Urton and is supported by additional structures found in the six khipus. This discovery could lead to a broader understanding of the social hierarchy of San Pedro de Corongo in 1670, as well as an expanded reading of the six Santa Valley khipus. Furthermore, this study presents the first-ever identification of recto and verso cord attachment knot orientations being used as a marked and unmarked sign, respectively. This article’s findings provide a significant contribution toward the ongoing decipherment of nonnumerical khipu signs.
Introduction
Khipus, or quipus, are knotted cord record-keeping devices best known for their use by the Inka Empire (ca. 1400–1532 CE), with origins dating back to at least the Middle Horizon (600–1000 CE; Conklin 1982). Even after the conquest of the Inka and the onset of Spanish colonialism, the use of khipu technology persisted (Salomon 2013), with modern khipus’ use documented in both functional and ritual contexts (Salomon 2004; Mackey 2002).
Spanish colonial sources report khipus being used in a multitude of ways: as letters sent across the empire, collections of census data, evidence in trials, and recordings of songs and histories, all of which could later be recounted by khipukamayuqs (khipu keepers or knot keepers; Conklin 2002: 54). Enticed by these colonial accounts and numerous archaeological specimens, Western interest in khipu function and decipherment was led by scholars such as Max Uhle (1897), L. Leland Locke (1912, 1923, 1927), and Erland Nordenskiöld (1925). It is Locke (1912) who is often credited with one of the most impactful advancements, demonstrating the expression of a knotted base-10 number system found on most Inka-style khipus, something only alluded to in general terms by Spanish chroniclers like El Inca Garcilaso de la Vega ([1609] 2006: 45). Drawing on this basic understanding of numerical khipu signs, other Western scholars began to illuminate an abundance of complex mathematical properties exhibited by knots tied on many Inka-style khipus (Ascher and Ascher [1981] 1997; Medrano and Khosla 2024).
More recently, however, researchers have increasingly pursued the decipherment of nonnumerical signs in Inka-style khipus (e.g., Clindaniel 2019; Hyland 2016), with one recent highlight being the potential discovery of a khipu-document “match”: six Inka-style khipus that record data similar to a 1670 colonial census document from the Santa Valley, Peru (Urton 2011, 2017; Medrano and Urton 2018). Despite heralding a potential breakthrough in khipu decipherment, some details surrounding these potential “Rosetta khipus” and their associated colonial document have either been excluded, ignored, or confused in the literature. Table 1 provides a reference for these six khipus using the naming conventions of the Open Khipu Repository.1
The aim of this article is to synthesize and evaluate what is known about this potential khipu-document “match” and to demonstrate how khipu decipherment can enrich our understanding of historical sources. Using combinatorics, this article identifies an optimal moiety alignment for the six pachacas, or lineage groups, listed in the 1670 colonial census—a method that offers a generalizable strategy for ethnohistorians working with other multilevel data sets. This moiety alignment differs from the one proposed by Manuel Medrano and Gary Urton (2018) and is supported by multiple additional structures found in the six khipus. Significantly, the discovery of this new moiety alignment may afford an expanded reading of the six Santa Valley khipus and enables the possible decipherment of several novel pieces of information: (1) the precise social hierarchy of the six pachacas of 1670 of San Pedro de Corongo, and (2) the first identification of the verso attachment knot orientation being used as an unmarked sign (to represent upper moiety affiliation) and the recto attachment knot orientation being used as a marked sign (to represent lower moiety affiliation).
A Brief History of the Study of the Santa Valley Khipus
The Santa Valley Khipu Archive
The six Santa Valley khipus were all apparently “found in the same tomb, somewhere in the Santa Valley” and were first studied by Carlos Radicati di Primeglio (1951, 1964)2 who acquired them “from an unknown person” (Radicati di Primeglio 2006: 158).3 These khipus’ shared context has led some to collectively call them the “Santa Valley khipus” and label them a khipu “archive” (Radicati di Primeglio 2006; Urton 2011), an idea that has recently been supported by radiocarbon dating (Ghezzi et al. 2023). Here, an archive refers to a collection of khipus related in space, time, and the data they encode.
Radicati was the first to recognize the six khipus as an archive, noting a similar cord structure and color pattern among them. He observed that each khipu presents “a constant series of six strings,” which form visually distinctive groups of identically colored cords (Radicati di Primeglio 2006: 158).4 These “six-cord groups” (Urton 2017: 221) are each composed of six adjacent pendant cords which share the same color scheme (fig. 1). This type of pendant cord color patterning is known as banding or color-banding (Salomon 2004: 167). In total, the six Santa Valley khipus are composed of 804 pendant cords, which can be divided into 133 six-cord groups like so: KH0323 has 48 six-cord groups, KH0324 has 9, KH0325 has 34, KH0326 has 17, KH0327 has 15, and KH0328 has 10.5 It is both the presumed shared context and structural similarity of the Santa Valley khipus that have led scholars to study them as a collective.
A Hypothesized Match
Though Carrie J. Brezine and Gary Urton studied the six Santa Valley khipus in 2005, it was not until six years later that similarities between the six khipus and a 1670 Spanish colonial revisita were formally noted (Urton 2011).6 The document, transcribed and published by Jorge Zevallos Quiñones (1991), pertains to a group of “Yndios Requayes” (Recuay Indians) who were resettled to the town of San Pedro de Corongo in the Santa Valley, Peru (Urton 2017: 218). The document states that each of the local 132 tributaries were required to pay 2 pesos, 7 reales and 3 quartillos. However, it is stated repeatedly that a total of 367 pesos, one-quarter real, and one quartillo is the total amount of tribute owed by the group as a whole.7 After discussing the tribute owed, the revisita includes a padrón (registry/census) that lists the names of 130 of the local tributaries (2 of the 132 tributaries are said to have been absent), with each name sorted into one of six distinct pachacas (Zevallos Quiñones 1991: 64).8 The term pachaca (one hundred) is likely used here to designate groupings at the level of the ayllu, which was “the essential socioeconomic unit of central Andean life . . . a corporate kin group that was often internally ranked” (D’Altroy 2015: 101). At this time the terms ayllu and pachaca were known to have been used interchangeably in the region (Zevallos Quiñones 1991: 11). Perhaps most importantly, the revisita states that, after the tribute owed had been announced to the local people, all of the information should be put into khipu(s) (“lo ponga por quipo” [Zevallos Quiñones 1991: 64]).
Using these three key pieces of information—the total amount of tribute owed, the list of named tributaries, and the mention of khipu(s) recording this information—Urton (2017: 217–39) suggests that the six Santa Valley khipus may be the ones referenced by the 1670 revisita, with each khipu recording the tribute of a pachaca. Urton (2017: 220–21) initially proposed two key arguments to support this hypothesis: (1) the organization of the Santa Valley khipus into 133 six-cord groups is nearly equivalent to the number of tributaries (132) discussed in the 1670 revisita, and (2) when the knot values of the first pendant cord from each of the 133 six-cord groups are added together, their total closely matches the total tribute owed (367 pesos) mentioned in the revisita. Although the number of six-cord groups (133) and tributaries (132) do not match exactly,9 Urton (2017: 222) contends that “we have already seen a near identical discrepancy between the number of tributaries listed in the San Pedro de Corongo padrón . . . and the number claimed in the text of the document.” He later calls these small discrepancies “on-the-ground ‘noise,’” which he believes was common among both Inka and colonial records alike (222). From here, Urton suggests that each six-cord group on the Santa Valley khipus may represent one of the tributaries recorded on the 1670 padrón, and that within each six-cord group, the first pendant cord recorded the amount of tribute paid by that individual.10
The link between six-cord groups and individuals is also supported by the work of Sabine Hyland (2016), who observed this phenomenon among Inka-style khipus used in Santiago de Anchucaya, Peru, to record labor obligations up until the 1940s. In addition, Jon Clindaniel (2019) has demonstrated a strong corpus-wide correlation between color-banding and individual-level data for Inka-style khipus.
Radiocarbon Dates for the Santa Valley Khipus
Importantly, this apparent khipu-document match coincides with several sets of radiocarbon dates taken from the six khipus, which suggest that they may predate the 1670 revisita (Cherkinsky and Urton 2014; Ghezzi et al. 2023).11 As a result, Sabine Hyland (2020a: 239) has asserted that the Santa khipus “were made significantly earlier than the tribute document and thus do not correspond to the aillu [sic] information in the colonial manuscript.” However, it is unclear if she is referring to the dates reported by Cherkinsky and Urton (2014) or to the two more recent Santa Valley khipu samples, radiocarbon dated for a 2020 khipu exhibition at the Museo de Arte de Lima (MALI). In either case, the MALI dates, publicly reported as calibrated dates in a brief feature from Google Arts and Culture, yield comparable date ranges to the previous samples.12
Significantly, Cherkinsky and Urton (2014: 35) qualify their dates, stating that “the imprecision of the calibrations” does not allow for “definite conclusions.” More recent Bayesian modeling, however, appears to corroborate the idea that the six khipus were likely made at least several decades before the 1670 colonial document (Ghezzi et al. 2023). Still, research on the accuracy of Andean radiocarbon dates continues; for the time being, the Santa Valley khipu dates, while internally consistent, are not entirely conclusive (Contreras 2022; Hogg et al. 2020: 775).
Rather than jettisoning the Santa Valley khipus from discussions of the 1670 revisita, taking the earlier radiocarbon dates at face value could instead indicate a pattern of khipu reuse. Alternatively, Ivan Ghezzi et al. (2023) have also suggested that the six Santa Valley khipus may record an earlier iteration of tributary collection from the people of San Pedro de Corongo. This hypothesis could also help to explain any small discrepancies between the 1670 document and the set of six khipus.
Some physical features support these hypotheses. Take, for instance, the presence of unknotted cords, or “ghost knots” as Frank Salomon (2004: 169) has referred to them, which are found on at least two of the Santa Valley khipus, KH0327 and KH0323 (Radicati di Primeglio 2006: 167). If color-banded khipus represent individual-level data (Hyland 2020a: 241), one would expect these khipus to have the most dynamic use-lives. Consequently, Medrano and Ashok Khosla (2024: 4) argue that untied knots may be used as a proxy for these low-level “working” khipus, and again, this pattern is known ethnographically from early twentieth-century khipu practices in Anchucaya, Peru, where each year “the knots on the khipus were untied so that the khipus could be re-used” (Hyland 2016: 14; emphasis added). Moreover, unknotted cords on color-banded khipus are not exclusive to the Santa Valley khipus. At least two other banded khipus, PC.WBC.2016.07 at the Dumbarton Oaks Museum in Washington, DC, and B366/1982.W.2157 (KH0597 in the OKR) at the Dallas Museum of Art in Texas, exhibit clear signs of unknotting. Additionally, Ghezzi et al. (2023) note that Radicati (2006: 160–61) described encountering many unattached premade pendant cords as he laid out the six khipus for the very first time. Ghezzi et al. (2023) propose that these premade cords suggest a more dynamic life cycle for the six khipus, in which they were actively being updated, likely with the most recent tribute information. Thus, the unknotted cords on the Santa Valley khipus, in tandem with the many unattached premade pendant cords encountered by Radicati, suggests that these khipus were used for an extended period of time before finally being encoded with information strikingly similar to that described in the 1670 colonial document.
Moiety Affiliation and Pendant Cord Attachment
Building upon an identified relationship between knot direction and moiety affiliation in a colonial khipu board (see Hyland, Ware, and Clark 2014), Medrano and Urton (2018) postulate that the pendant cord attachment knots on the Santa Valley khipus may indicate the moiety affiliation (hanan or hurin) of each tributary discussed in the 1670 revisita. This kind of “complementary opposition” has long been an integral part of the Andean worldview, evident as far back as the Early Horizon (900 BCE–200 BCE), if not earlier (Burger and Salazar-Burger 1993). Moiety-based social organization was particularly prevalent during the reign of the Inka (Pärssinen 1992; Zuidema 1964), continuing through the colonial era (Hyland, Ware, and Clark 2014; Wernke 2013), and, in some places, persists even to this day (Salomon 2004). The two halves—usually referred to as hanan (upper, superior/primary) and hurin (lower, inferior/secondary)—are often composed of local ayllus (or in this case pachacas). Generally, half of the ayllus belong to hanan and half to hurin. Additionally, ayllus are often ranked within each moiety, adding a secondary level of hierarchy (Pärssinen 1992; Urton 1993; Zuidema 1964; Wernke 2013). This multilevel hierarchy “constituted an order of priority and prestige” among ayllus that is “played out in local social, political, and ritual relations and practices” (Urton 2017: 39).
The two orientations of a typical pendant cord attachment knot, labeled as either “recto” or “verso,” make it perfectly suited for recording binary information such as moiety affiliation (fig. 2).13 Note that to consistently label attachment knots as recto or verso, the orientation of a khipu and direction of its study is crucial. Helpfully, a standard method for recording khipus has been developed, starting from the knotted, tasseled, or doubled end of the primary cord and moving toward the “dangle” or tail end of the primary cord (Conklin 2002: 68).
Taking the first pendant cord in each six-cord group on the Santa Valley khipus as the “identifier” cord for that group (fig. 3), Medrano and Urton (2018) found a total of sixty-three recto groups and seventy verso groups. Medrano and Urton (2018) then separated the six pachacas from the 1670 revisita—named Namus, Corongo, Cuyuchin, Cusca, Guauyan, and Ucore—into proposed moieties. Based on the padrón, each pachaca contained a number of named tributaries—Namus (eighteen tributaries), Corongo (twenty-three), Cuyuchin (nine), Cusca (seven), Guauyan (forty-one), Ucore (thirty-two)—that Medrano and Urton (2018) argued, when totaled with two other pachacas placed within the same proposed moiety, should come close to the number of recto and verso groups observed on the six Santa Valley khipus. From there, Medrano and Urton (2018) posit that the seventy verso groups are linked to the Corongo, Guauyan, and Cusca pachacas, whose named tributaries in the padrón total to seventy-one, and that the sixty-three recto groups are linked to the Namus, Cuyuchin, and Ucore pachacas, whose named tributaries in the padrón total to fifty-nine (table 2). Importantly, Medrano and Urton (2018) relax Urton’s (2011, 2017) original hypothesis of a one-to-one correspondence between each of the six khipus and the six pachacas. Instead, they argue that tributaries may have been divided among khipus based on other means, such as total tribute contribution, and thus they assess their proposed moiety affiliations using combined cord attachment data from all six khipus (Medrano and Urton 2018: 13).
The six-cord groups on each of the Santa Valley khipus are attached exclusively as either all recto or all verso for that khipu, with one exception: KH0326 begins with fifty-nine verso attachments before switching to a mix of recto and verso attachments after a space between pendants on its primary cord. Another peculiarity of KH0326 is its tenth six-cord group, which actually includes ten contiguous brown cords, appearing to temporally break from the standard six-cord banding pattern. Medrano and Urton (2018) set aside the last four brown cords, taking the first six brown cords as its own six-cord group and reading the group’s “identifier” cord as verso. According to them, this approach best adheres to the numerical patterns observed in KH0326 and the other five Santa Valley khipus. It also avoids splitting the ten cords into two groups and repeating colors across consecutive cord groups, which is also inconsistent with the color-banding pattern seen in KH0326 and the other five khipus. Therefore, following Medrano and Urton (2018), the “identifier” cords for KH0326 can be read as (R = Recto and V = Verso): V, V, V, V, V, V, V, V, V, V, R, R, R, V, V, R, R.
Reexamining Moiety Affiliation
While Medrano and Urton’s (2018) moiety alignment yields groupings of tributaries similarly sized to that of the observed recto and verso groups on the six Santa Valley khipus, it still results in an absolute difference of five from the observed values.14 Of course, some difference is expected, with only 130 names listed on the padrón and 133 six-cord groups on the six khipus. While Medrano and Urton (2018: 9) argue that their moiety alignment is statistically significant, this article contends that a better-suited moiety alignment may be derived. However, like Medrano and Urton (2018), this article does not seek to draw one-to-one correspondences between any of the six khipus and the six pachacas.
Finding an Ideal Moiety Alignment with Combinatorics
Rather than employing a “guess and check” method, combinatorics can be used to generate every possible moiety combination. Since the six pachacas need to be grouped into two separate moieties (i.e., two groups of three), the total number of ways to do so is equivalent to the number of unique (unordered) ways to combine three of the six pachacas. In other words, the total number of ways to combine three of six pachacas is C(6, 3), or “6 choose 3,” which yields twenty possible combinations (table 3).15 For each potential moiety combination, one can compute the absolute difference (or error) from the observed recto/verso count and the probability p of observing the produced correlation—that is, if the attachment knots of the “identifier” cords for the 133 six-cord groups were randomly attached as either recto or verso.
After computing every possible combination, it is clear that there are three moiety alignments, including that proposed by Medrano and Urton (2018), which yield apparently statistically significant results (p < 0.05). One of these alignments produces the same p-value (0.04478) as that given by Medrano and Urton’s (2018) alignment. The third, however, yields a p-value of 0.02985, indicating a less than 3 percent probability of the observed correlation occurring by chance alone. Although all three potential moiety alignments may be statistically significant, it is this last, novel alignment that yields the smallest possible absolute difference when compared to the actual recto/verso count.
Applying this new moiety alignment yields a “verso” moiety of Namus, Cuyuchin, and Guauyan and a “recto” moiety of Corongo, Cusca, and Ucore (table 4), and has several important implications. First, the newly proposed moiety alignment yields an absolute difference of three from the observed recto/verso attachments, making it the closest possible alignment for the known data.16 Second, the new alignment may reveal familiar bipartite/tripartite Andean hierarchies within the pachacas listed on the 1670 revisita. Third, with this new moiety alignment, not only is one able to speculate which pachacas belong to the same moiety, as Medrano and Urton (2018) did, but one could even posit to which moiety in particular, either hanan (upper) or hurin (lower), each pachaca belonged to. In doing so, this article proposes a decipherment for which attachment knot orientation (verso/recto) was used to signify each moiety (hanan/hurin) in the case of the six Santa Valley khipus. Finally, by joining all three observations, it may be possible to reconstruct a secondary layer of social hierarchy, the internal ranking for the six pachacas of 1670 San Pedro de Corongo.
This approach may seem, at first glance, to condense Andean communities into measurable mathematical units. However, this article’s aim is to formulate hypotheses about the social organization of these communities by drawing from the already simplified representations found in the historical records of both Andean and Spanish administrators. Therefore such mathematical and combinatorial methods are useful not because they simplify but rather because they may help dimensionalize flattened colonial portrayals of Andean communities.
An Ideal Alignment
The newly proposed moiety alignment minimizes the difference between the number of names on the revisita (130) and the number of six-cord groups on the six Santa Valley khipus (133) to just three. Importantly, this small discrepancy may be resolved in a similar manner to that employed by Medrano and Urton (2018) when trying to address their alignment’s absolute error of 5.
First, if we hypothesize for the newly derived moiety alignment that both of the “absent” tributaries discussed in the revisita may have belonged to the “verso” moiety, then the number of tributaries linked to verso cord groups in the new alignment can be bumped up from 68 to 70 individuals. Second, note that the six khipus contain 133 six-cord groups, whereas the revisita only discusses 132 tributaries. Therefore, there is no way to ever discern “to which khipu the extra six-cord group would have pertained” (Medrano and Urton 2018: 9). By subtracting the “extra” recto six-cord group from the total recto cord group count, the result is 62 tributaries linked to 62 recto cord groups. In other words, the counts given by the newly derived moiety alignment now match exactly, creating an ideal alignment with 70 tributaries linked to 70 verso cord groups and 62 tributaries linked to 62 recto cord groups.
A Familiar Bipartite and Tripartite Hierarchy
Aside from minimizing alignment error, the newly proposed moiety alignment may also reveal a bipartite/tripartite social structure among the six pachacas. Taking the order by which the 1670 revisita lists the six pachacas, one can assign a positional number to each, like so: (1) Namus, (2) Corongo, (3) Cuyuchin, (4) Cusca, (5) Guauyan, and (6) Ucore. Using the pachacas’ assigned positional numbers as placeholders, the new alignment yields a “verso” moiety of {1, 3, 5} and a “recto” moiety of {2, 4, 6}. Notice that the two sets created—{1, 3, 5} and {2, 4, 6}—are composed of either all odd or all even positional numbers. Therefore, the new moiety alignment places every other pachaca—as listed on the padrón—into the opposite moiety of the pachaca listed before and after it. The listing of moiety affiliation creates a balanced pairing effect, or duality, between the two moieties, with each pachaca from the “verso” moiety always followed by a reciprocal pachaca from the “recto” moiety. The paired pachacas also appear to contain similar numbers of tributaries. For example, Namus (a “verso” pachaca) has eighteen tributaries and Corongo (the “recto” pachaca following Namus in the padrón) has twenty-three tributaries. Similarly, the two largest pachacas, Guauyan (41) and Ucore (32), and the two smallest pachacas, Cuyuchin (9) and Cusca (7), appear paired together. Therefore, aside from the bipartite moiety level division between pachacas, a secondary tripartite social structure is formed, made up of three distinct pairs of pachacas, with each pair first containing a “verso” pachaca followed by a “recto” pachaca (table 5).
How the pachacas were paired and ranked may have been influenced by their geographic placement before the establishment of San Pedro de Corongo, and the many other reducciones mandated by Francisco de Toledo in the 1570s. Notably, in 1543, Cristobal Ponce de Leon visited several neighboring villages in this region (Cook 1977), some of which had names resembling five of the pachacas mentioned in the 1670 revisita. Interestingly, the sequence in which Cristobal Ponce de Leon visited these similarly named villages loosely corresponds to a reverse ordering of the pachacas as listed in the 1670 revisita, like so: Urcos, Guauya, Cuzca, Llamuz, and Corongo (Cook 1977: 30).
Similar bipartite/tripartite models found in Quechua linguistics suggest that this pachacha organization aligns well with other Andean cultural practices. Take the number six (suqta) for instance. Aside from suqta, the number six may also be referenced as kinsa kinsa (three [plus] three) or iskay kinsa (two [times] three; Urton and Llanos 1997: 228). The separation of the six pachacas into two sets of three, via “verso” and “recto” moiety affiliations, echoes the bipartite notion of kinsa kinsa (three plus three), whereas the pairing of reciprocal “verso” and “recto” pachacas parallels the tripartite notion of iskay kinsa (two times three).
Additionally, social and political bipartite/tripartite organizations were common under Inka rule (Pärssinen 1992). In fact, the pachaca divisions theorized above are reminiscent of Inka social structures illustrated by Reiner Tom Zuidema (1964), who noted several nested bipartite/tripartite divisions in his outline of the ceque system. He argued that the city of Cuzco was divided into hanan and hurin halves, with each half being made of two other ranked halves. These inner halves, or quarters, were then further divided into three ranked parts labeled Collana, Payan, Cayao. For Zuidema (1964: 42), this tripartite division corresponded to a social hierarchy, with Collana on the top, Payan in the middle, and Cayao at the bottom. Of course, one should be wary of applying the social landscape of the Inka Capital to San Pedro de Corongo over one hundred years later. However, Steven A. Wernke (2013: 226) notes that in some regions, like the Colca Valley, “the reducciones and post-Toledan political and economic administration were clearly based on preceding Inka-era networks of ayllu affiliation and authority.” Thus, it could be argued that the three pairs of pachacas derived from the newly proposed moiety alignment closely mirror a Collana, Payan, Cayao system, with the first pair of pachacas listed on the 1670 padrón corresponding to the idea of Collana, the second pair to Payan, and the third pair to Cayao.
Yet what incentive would a Spanish scribe have to record the six pachacas in this particularly Andean order? It may be that the ordering of the six pachacas on the padrón was relayed to the Spanish scribe by an Indigenous informant (or multiple). This could explain why the padrón only lists 130 names, yet the scribe was apparently aware that two additional tributaries were absent from the count. An Indigenous informant would also increase the likelihood that the ordering of both the pachacas and names within those pachacas on the padrón held hierarchical significance, with higher-ranking tributaries being listed first.
If this were the case, one may expect someone like Po ticlla condor, the first individual listed on the padrón, to have held a position of power. Perhaps Po ticlla condor was the local cacique principal, or head of the most powerful lineage in the area, in this case the pachaca Namus. A position such as this would have certainly given Po ticlla condor the authority to recount the ordering of the six pachacas to the author of the 1670 revisita.
Importantly, scribal marks found on the original colonial document, not appearing in Zevallos Quiñones’s (1991) transcription, hint at a variation of this interpretation.17 A note written just before Po ticlla condor’s name on the padrón reads “muerto” (dead), indicating his passing.18Po ticlla condor is also the only individual whose name is followed by a cross, yet another indicator of his passing. So why then, would Po ticlla condor be listed as a tributary on the padrón if he was no longer alive? If Po ticlla condor had passed away around the time of the revisita, perhaps it was Lorenso tapia, listed second on the padrón, who was tasked with recounting the order of pachacas to the scribe. Lorenso tapia may have had Po ticlla condor added to the padrón out of respect, or maybe the local people were still responsible for Po ticlla condor’s tribute. Either way, the implication is still that Po ticlla condor held a position of power.
Theorizing the Hierarchical Relationships of the Pachacas and Recto/Verso Attachments
With a potential bipartite/tripartite social structure derived for the six pachacas, it may now be possible to theorize which moiety in particular—either hanan or hurin—each pachaca belongs, as well as which khipu pendant cord attachment orientation—either verso or recto—was used to signify each moiety group. To help interpret this relationship it will be useful to review the concept of markedness, as developed by Nikolai Trubetzkoy and Roman Jakobson in the 1930s (Andersen 1989). Markedness refers to “the relation between linked pairs or dyadic sets of phonological or grammatical elements, or word meanings, that are in a relationship of asymmetrical (hierarchical) binary opposition to each other” (Urton 2003: 144). In other words, an unmarked group often serves as a more general, default category, whereas a marked group identifies an oppositionaly related, secondary category. For example, in the word pair of day (unmarked) and night (marked), the word day may refer to when it is light or a full twenty-four-hour period, whereas the word night only refers to when it is dark (Clindaniel 2019: 13–14).
Previous khipu scholars have made use of markedness theory, identifying instances of other marked/unmarked binary signs within Inka-style khipus (e.g., Urton 2003; Hyland 2014; Clindaniel 2019). Jon Clindaniel (2019: 34) notes that postconquest Inka-style khipus made use of “S- and Z-knots, S- and Z-plied cords, Recto and Verso cord attachments, as well as color seriation and color banding in binary opposition to one another as unmarked/marked pairs.” Yet, of the four binary signs highlighted by Clindaniel, scholars have only successfully disentangled examples of hierarchical relationships for three (see Hyland, Ware, and Clark 2014; Hyland 2014; Clindaniel 2019; Hyland 2016), leaving recto and verso pendant cord attachments without an instance of hierarchical decipherment. As Clindaniel (2019: 15) points out, by using the moiety alignment derived by Medrano and Urton (2018), “it is not known which attachment type would have been considered marked and which unmarked on the basis of these proposed groupings alone.” Yet herein lies the potential of the newly proposed moiety alignment, for one can theorize which attachment orientation (recto/verso) was considered marked—and which was considered unmarked——for the people of 1670 San Pedro de Corongo.
To propose a hierarchical decipherment for the two pendant cord attachment orientations, it is important to highlight two major facets of unmarked/marked pairings: completion and asymmetry. Completion, for example, can be seen when discussing finger positions among certain Quechua-speaking groups. Each finger is paired with another so that “the odd number fingers ‘one’ and ‘three’ are accompanied, or made complete by the following even numbered fingers ‘two’ and ‘four’ (the little finger is termed ‘youngest finger’)” (Urton and Llanos 1997: 61–63). Within each finger pair, it is sometimes only the odd-numbered fingers (i.e., thumb, middle, and little fingers) that are named directly, with the even fingers (i.e., index and ring fingers) simply being labeled as “following, or accompanying finger” (75). In this way, the odd-numbered fingers are unmarked (primary) while the even number fingers are marked (secondary), being defined by their relationship with the odd finger to which they are paired. The odd/even pairing of the pachacas on the padrón may communicate a similar notion of completion. Much like an odd-numbered finger is “made complete” by the following even numbered finger, perhaps so too is each “verso” pachaca “made complete” by its following “recto” pachaca.
For asymmetry, take the example of the Quechua word khallu (unmarked), meaning “one alone.” Bruce Mannheim (1986: 60) has noted that in Quechua, marked words are often “semantically more complex” than their unmarked counterparts. By simply adding the suffix -ntin, khallu can be transformed into its marked form khalluntin, meaning “the one together with its mate/pair.” Note that “the ‘mate’ is possessed by the primary character. That is, in the khallu/khalluntin formulation, the ‘two’ (or ‘second’) is possessed by the ‘one’ (or ‘first’) in the formation and meaning of the pair” (Urton and Llanos 1997: 65). Thus, while this relationship also highlights the importance of pairs, with the need for the “one alone” to find “its mate/pair,” it carries a sense of assumed “possession” or asymmetry within said pair.
Drawing from these relationships of marked/unmarked linguistic pairs in the Quechua language, one may posit that each pachaca pairing follows a similar structure: the pachacha listed first could serve as the primary (unmarked) pachaca, whereas the pachaca listed second could serve as the secondary (marked) pachaca, (i.e., the first pachaca’s “mate”). Since the pachaca listed first within each of the three pachaca pairings has been assigned to the “verso” moiety, it would follow that these “verso” pachacas are the primary, or unmarked group, while the “recto” pachacas which follow them serve as the secondary, or marked group. In this way, similar to the khallu/khalluntin example, the “verso” pachaca may be thought of as dominant over, or as “possessing,” the “recto” pachaca.
It seems, then, that the six Santa Valley khipus use verso attachments to denote the principal, unmarked category, while recto attachments are used to denote the secondary, marked category. Therefore, this article proposes that, at least for the six Santa Valley khipus, a verso cord attachment for the “identifier” cord of a six-cord group may have signified that an individual referenced by it belonged to the hanan (or “upper,” unmarked) moiety, while a recto cord attachment for the “identifier” cord of a six-cord group may have implied an individual’s membership to the hurin (or “lower,” marked) moiety. In other words, this article proposes the following relationships:
Verso = Unmarked = Hanan = Upper Moiety = Primary
Recto = Marked = Hurin = Lower Moiety = Secondary
With this possible decipherment of recto and verso attachments for the six Santa Valley khipus, coupled with the potential pachaca pairs, it is possible to postulate the precise hierarchical social ordering of the six pachacas of the 1670 San Pedro de Corongo. It would seem that the six pachacas are listed on the padrón in social rank order, both by moiety as well as within said moieties. In other words, the pachacas are listed alternating: hanan, hurin, hanan, hurin, hanan, hurin, but even more so, that they are listed hierarchically as: upper hanan, upper hurin, middle hanan, middle hurin, bottom hanan, bottom hurin (table 6). It is worth reiterating that within this proposed hierarchy, each pachaca is paired with a reciprocal pachaca from the opposite moiety of similar size. Thus, not only can the six pachacas of San Pedro de Corongo potentially be sorted into separate moieties, as shown by Medrano and Urton (2018), but it is also possible to theorize which moiety in particular—either hanan (unmarked) or hurin (marked)—each pachaca belongs to, as well as which khipu pendant cord attachment type—either verso (unmarked) or recto (marked)—was used to signify each moiety group in the six Santa Valley khipus.
Additionally, this possible decipherment may reveal an asymmetrical distribution of the actual tribute paid by each moiety, again, data that were not recorded by the 1670 revisita (Medrano and Urton 2018: 13–16; Urton 2017: 232–35). Recall that it was previously hypothesized that the knot value of the first cord in each six-cord group (the “identifier” cord) represents the tribute paid by each individual (Urton 2017: 220–21). Therefore, in total, the khipus record the “verso” moiety (i.e., Namus, Cuyuchin, and Guauyan) as having paid 381 pesos, whereas the “recto” moiety (i.e., Corongo, Cusca, and Ucore) only appears to have paid 86 pesos.19 At the individual level, each member of the “verso” moiety paid on average about 5.45 pesos compared to an average of about 1.4 pesos paid by each member of the “recto” moiety. Such an asymmetrical distribution of tribute payments may hint at negotiations or agreements made between the two moieties (Urton 2017: 232–35). If this were the case, such social bartering was apparently unknown to, or deemed unimportant by, the Spanish scribe of the 1670 document.
Further Evidence for the Proposed Decipherment
The newly proposed moiety alignment, and the designation of hanan (unmarked) affiliation through verso attachments and hurin (marked) affiliation through recto attachments, can also be corroborated by other structures embedded in the six Santa Valley khipus. These include (1) the frequency of recto/verso attachments found on the Santa Valley khipus, (2) the primacy of the verso cords on KH0326, and (3) an unmarked/marked relationship suggested by the kayte of KH0327 and KH0323.
First, as a simple check, Urton (2003: 145) has suggested that for paired khipu signs, the unmarked (default) sign will occur more frequently than its paired marked sign. This notion is clearly reflected in the Santa Valley khipus, which have a higher frequency of verso attachments when compared to recto attachments.
Second, the mix of recto and verso attachments found on KH0326 allows us to further test the hanan (unmarked) decipherment of verso attachments. Note that the verso attached cords on KH0326 are primarily located on the first half of the primary cord, followed by a gap and then a majority of recto cords. While the presence of both recto and verso attachments on KH0326 appears to record tribute payments from members of both moieties, this in no way necessitates the existence of a “mixed” ayllu containing members from both moieties. In fact, Medrano and Urton (2018: 16) instead posit that the mix of both attachment types found on KH0326 could be explained by a “by tribute paid” sorting system by which KH0326 constitutes “some sort of ‘remainder’ category,” with odd tributaries from both the hanan and hurin moieties being recorded together for purely administrative purposes. Therefore the primacy of the verso cords on KH0326 is signaled both spatially, by their position along the primary cord (i.e., appearing first), and also through their verso knot attachments. Garcilaso de la Vega ([1609] 2006: 46) discusses the importance of spatially ranked ordering in khipu cords, noting that “objects that had no special colors were arranged in order, beginning with the most important and proceeding to the least.” This type of data redundancy, through both signs and spatial positioning, has been similarly noted by Hyland. In a modern herding khipu collected by Max Uhle, Hyland (2014: 645) observed that while S-twist cords were used to signify female sheep and Z-twist cords were used to signify male sheep, these two categories were also separated spatially.
Finally, the tassels, or kaytes (also caytes), found among the Santa Valley khipus may signal both their genre, as tributary khipus, while also hinting at moiety affiliation. Although Salomon (2004: 274) wrote that “three of Radicati’s six [Santa Valley khipu] have knobs or tufts . . . at the redoubled end of their main cords,” and later Hyland (2020b: 152) wrote that “only one of the six Santa Valley khipus analysed by Urton has a kayte,” there are actually two Santa Valley khipus, KH0327 and KH0323, which bear kaytes at the start of their primary cords (Radicati di Primeglio 2006: 163).20 Hyland (2020b) has suggested that kaytes may signify the genre of Inka-style khipus, and she has already compared the orange and yellow kayte found on KH0323 with a similar kayte found on a 1930s labor accounting khipu from Anchucaya (Hyland 2016, 2020a).
Yet, aside from simply denoting genre, perhaps the kaytes of KH0327 and KH0323 were also used to signal moiety affiliation. In line with the verso/hanan and recto/hurin hypothesis, KH0327, which contains only verso (unmarked) pendant cords, bears a monochrome pale yellow tassel, while KH0323, which contains only recto (marked) pendant cords, bears the dual-colored pale yellow and dark orange tassel. Thus, similar to how adding the suffix -ntin to khallu transforms it from an unmarked to a marked word (i.e., khalluntin), the yellow tassel may be viewed as signaling an unmarked category, whereas the addition of orange to the tassel may transform it to signal a marked category. The use of a lightly colored tassel to represent an unmarked category (the hanan moiety) and the mix of a light and dark color to represent a marked category (the hurin moiety) is also consistent with Clindaniel’s findings on color and markedness among Inka-era khipu pendant cords. Clindaniel (2019: 88) hypothesizes a “hierarchical relationship” between pendant cord color categories in which solid light colors are ranked the highest, followed by mottled colors, barber-poled colors, and, last, solid dark colors. Although this typology is not a clean binary, these “transitional colors,” between solid light (unmarked) and solid dark (marked), “can then be hierarchically conceived as more marked than light colors, but less marked than dark colors” (Clindaniel 2019: 82). Therefore, the kayte of KH0327 and KH0323 may signal both their genre, as tributary khipus, while also hinting at moiety affiliation.
Cord Color and Tributary Identity
With the pachaca-level hierarchy hypothesized by this article for 1670 San Pedro de Corongo, the next logical step is attempting to match Santa Valley khipu data directly with each tributary named in the 1670 revisita. On this front, Medrano and Urton (2018: 18–19) speculate that the color of each six-cord group could carry information pertaining to individuals such as their names, noting thirty-two unique color combinations among the six-cord groups on Santa Valley khipus and thirty unique first names in the padrón. If their hypothesis is correct, then a numerical correlation between the number of unique first names and unique color combinations should still hold within the moieties themselves. Therefore, to test their theory, this article separates the unique first names as well as the unique color patterns into their respective moiety affiliations based on the new alignment.
Unfortunately, the new moiety alignment results in a “verso” moiety with twenty-three unique first names in conjunction with twenty-seven unique color patterns, and a “recto” moiety with twenty-five unique first names in conjunction with only fourteen unique color patterns. Yet an examination of these discrepancies reveals that they are not attributable to the newly proposed moiety alignment suggested in this article but instead stem from the lack of color diversity found within the Santa Valley khipus that contain recto cords. While the four Santa Valley khipus containing verso cords (KH0324, KH0325, KH0326, KH0327) carry over 81 percent of all the color patterns seen across all the six khipus, the three khipus that contain recto cords (KH0323, KH0326, and KH0328) carry less than 44 percent of the color patterns seen across all six khipus.21
The lack of color diversity among the Santa Valley khipus with recto cords lies in the repetition of color patterns on the two entirely recto khipus, KH0323 and KH0328. On KH0328, for instance, the color patterns of cord groups 1–5 (LG-W, RL, AB, W, RB) are repeated, in the same order, in cord groups 6–10.22 In fact, both KH0323 and KH0328 exhibit what could be called “seriated-banding,” in which cords are split into color bands, with those larger color bands then repeating in a seriated fashion across a single khipu (fig. 4).23 The seriated-banding on KH0323 is most apparent in the second half of the khipu, where the color bands of W, RB, AB, YB are clearly repeated four times in a row in cord groups 33–48 and may even appear earlier in cord groups 21–32.24 While colors recorded for the earlier sections of KH0323 may not exactly match the later seriated pattern, the slight discrepancies in colors likely come from the subjective nature by which scholars record khipu color.25
Based on these observations of color/name frequencies and of seriated-banding, it does not seem likely that KH0323 and KH0328 used color to directly sign names. Rather, the seriated-banding in KH0323 and KH0328 may encode other important Andean structures, such as the internal social hierarchies of a moiety or pachaca/ayllu. In highland Tupicocha, Peru, for example, Salomon (2004: 189–92) notes that ayllu-internal paperwork commonly lists members by seniority, and he suggests that ayllu members may have been similarly seriated within khipus according to rank. While the lack of evidence for KH0323 and KH0328 to be directly recording names with color does not completely negate a similar idea for the verso Santa Valley khipus, it is certainly not very supportive.
Perhaps, rather than color, or color alone, other means were used in combination to denote each individual. For instance, Radicati reported finding “strands of human hair mixed with the cotton fiber on some cords” while studying KH0325 and KH0326 (Radicati di Primeglio 2006: 165). Human hair in khipu construction is not unheard of, with several cords from Laguna de los Cóndores containing human hair (Urton 2007), and at least one khipu, studied by Hugo Pereyra Sánchez (1999), being constructed almost entirely from human hair. Perhaps human hair, whether symbolically or practically, aided khipukamayuq(s) in their representation of individuals.
Conclusions
Through the use of combinatorics, this article has demonstrated that an optimal moiety alignment exists for the six pachacas of 1670 San Pedro de Corongo—different from that proposed by Medrano and Urton (2018)—and can be corroborated by additional structures found in the six Santa Valley khipus. The discovery of this new alignment may afford an expanded reading of these khipus and has led to the possible decipherment of several novel pieces of information: (1) the exact social hierarchy of the six pachacas of 1670 San Pedro de Corongo, and (2) the first identification of the verso attachment being used as an unmarked sign (to represent the hanan moiety) and the recto attachment being used as a marked sign (to represent the hurin moiety).
Moreover, the use of combinatorics may offer a generalizable strategy for ethnohistorians working with other multilevel data sets. Attempting to decipher the Santa Valley khipus will only aid in our understanding of similarly structured khipus and allow for the further refinement of the historical record in tandem with historic documents. For instance, khipu KH0055 is color-banded and bears several six-cord groups that appear to follow many of the same notational principles identified in the Santa Valley khipus.26
Importantly, the enrichment of the 1670 colonial document by means of six Inka-style khipu presents a unique case, one in which the study of Indigenous records (i.e., khipu) can be used to inform a colonial document—and, in the process, our understanding of Indigenous practices, lifeways, and materials. This is particularly relevant for areas, like that surrounding San Pedro de Corongo, that still lack sufficient archival documentation for this time period (León Gómez 2018: 23). Now, the once simple list of tributaries on the 1670 revisita may be enriched by notions of complex social hierarchies, nuanced by local tribute payment agreements and negotiations.
Furthering our understanding of the Santa Valley khipus should inspire continued searches for additional pertinent colonial documents, as well as more research into the colonial-era transformations of the Santa Valley. Until other possible khipu-document matches are brought to light, the six Santa Valley khipus, in conjunction with the 1670 revisita of San Pedro de Corongo, remain a highly promising opportunity for the decipherment of nonnumerical khipu signs.
I am grateful to Idabelle Paterson, Manuel Medrano, Dr. Jon Clindaniel, Dr. Bill Fash, Dr. Matt Liebmann, Dr. Jason Ur, and my numerous colleagues who provided thoughtful comments on earlier drafts of this article.
Notes
The Open Khipu Repository, Zenodo, 26 July 2022, https://doi.org/10.5281/zenodo.6908343.
The six khipus now belong to the Biblioteca Museo Temple Radicati collection in Lima, Peru (Medrano 2021).
All translations are my own unless otherwise noted.
Radicati (2006: 216) believed six-cord groups were the key to khipu decipherment, and he argued that each color band, in combination with its knots, could be viewed as an ideogram, though this idea has not been adopted more broadly.
Note that 133 × 6 = 798, not 804; six pendant cords do not belong to six-cord groups.
A revisita (revisit) was a Spanish colonial administrative procedure for gathering new census data to reassess tribute requirements based on population size (Urton 2017: 218).
This is slightly more than the approximately 363 pesos owed if each tributary paid their full 2 pesos, 7 reales, and 3 quartillos.
The list of names has been reproduced several times (see Zevallos Quiñones 1991; Urton 2017; Medrano and Urton 2018).
Recall that the 1670 revisita states that there are 132 taxpayers of San Pedro de Corongo, yet only explicitly lists 130 of their names.
One can only speculate regarding the meaning of the remaining five cords in each six-cord group; it may be that they recorded additional forms of tribute other than currency (Urton 2017: 230–33).
See also “Khipus and Written Documents,” Google Arts and Culture, https://artsandculture.google.com/story/TwURueXdUOqKzA?hl=en (accessed 7 March 2023).
“Khipus and Written Documents.”
This knot is commonly known as a cow hitch or lark’s-head knot.
Corongo, Guauyan, and Cusca sum to within one of the number of verso attachments, and Namus, Cuyuchin, and Ucore sum to within four of the number of recto attachments.
There are “n choose k” ways to choose an (unordered) subset of k elements from a fixed set of n elements, where “n choose k” = C(n, k)=n!/(k!(n-k)!).
There are 133 six-cord groups and 130 tributary names listed on the 1670 revisita, so |133–130| = 3. In the newly proposed moiety alignment, there are 70 verso six-cord groups matched with 68 tributaries and 63 recto six-cord groups matched with 62 tributaries. Therefore, |70–68| + |63–62| = 2 + 1 = 3.
Two previously unmentioned scribal marks on the padrón are the word ojo written before the names juo po haçaña hijo de coxo and po joseph hijo del coxo, suggesting the scribe had a reason to draw attention to these two individuals.
Adan Ramirez-Figueroa, pers. comm., 25 February 2022.
The total verso tribute amount is unknown due to broken cords, but is likely 381 or 382 pesos (Urton 2017: 229).
KH0327 and KH0323 are also the only two Santa Valley khipus with Z-twisted primary cords and primary cords involving nested barber pole color patterns.
Note that 81 percent and 44 percent do not make 100 percent due to the overlap of color patterns across the mixed recto and verso khipu KH0326.
Capitalized letters are used to represent yarn colors (e.g., W = white and AB = light brown), which can then be combined in several ways (e.g.,- = barber-poled, : = mottled, and / = segmented). Therefore, “W-AB” represents a white and light brown barber-poled cord.
Lucrezia Milillo (2020: 268, 272) has noted a similar patterning on a khipu from the Pigorini Museum in Rome, which contains “a seriation of paired colour bands.”
For a table showing these repetitions, see Radicati di Primeglio 2006: 204.
For example, the colors recorded for the Santa Valley khipus in 2005 by Carrie J. Brezine and Gary Urton do not always match those recorded by Radicati di Primeglio (2006).
The value of each pendant cord seems to loosely adhere to a set of numerical relations based on that cord’s position within its six-cord group (see Urton 2017: 227). Additionally, for both KH0055 and the six Santa Valley khipus, the first and last cord within each six-cord group does not bear any subsidiary attachments.
