Inka administration in Tawantinsuyu by means of the knotted-cords

GARY URTON

In each provincial center they had accountants who were called “knot- keepersorderers” Iquiposcamayos], and by means of these knots they kept the record and account of what had been given in tribute by those [people] in that district, from the silver, gold, clothing, herd animals, to the wool and other things down to the smallest items, and by the same knots they commissioned a record of what was given over one year, or ten or twenty years and they kept the accounts so well that they did not lose a pair of sandals.¹

To read Cieza de Leon's account, it would seem that the Inkas had devised a remarkably efficient system for overseeing the collection, management, and disposal of goods and resources in settlements throughout the provinces of their vast empire, which stretched some 5,000 kilometers along the spine of the Andes, from the border between present-day Ecuador and Colombia southward to central Chile (Map 9.1).

Thanks to Helmut Schindler for his help and kind hospitality during my two-week visit to the Museum fur Volkerkunde, Munich, in the summer, 2004. I also express my profound appreciation to Carrie Brezine, who provided me with the breakdown and initial structural analysis of khipu UR 28. Brezine was, at the time, administrator for the Khipu Database project. The further interpretation and analysis of that khipu in the form presented herein is the work of the author.

¹ Cieza de Leon, El Seiiorio de los Incas, Cieza de Leon (trans.) (Lima: Instituto de Estudios Peruanos, 1967), p.

² Marcia Ascher and Robert Ascher, Mathematics of the Incas: Code of the Quipus (New York: Dover, 1997); William J. Conklin, “A Khipu Information String Theory,” in Jeffery Quilter and Gary Urton (eds.), Narrative Threads: Accounting and Recounting in Andean Khipu (Austin: University of Texas Press, 2002), pp. 53-86; and Gary Urton, Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records (Austin: University of Texas Press, 2003).

GARY URTON

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Map 9.i Tawantinsuyu - approximate extent of the Inka Empire with inset map of the approximate boundaries of the four suyus (quadrants).

how these colorful knotted-cords could have encoded such a wide variety of information, and in as complex an array of forms, as is claimed for them by Cieza and a host of other Spanish commentators. The question, then, is not only whether we can document with Spanish testimony but demonstrate as well that Inka cord-keeping was highly efficient and effective. In order to attempt to address this basic challenge, we begin by acknowledging a few basic circumstances that limit our ability to identify and evaluate critically the characteristics of this accounting system.

Whatever its indigenous components and characteristics, as a functioning and effective set of institutions and practices of accounting and controls, the Inka administrative system had all but collapsed over the first few decades following the Spanish Conquest, which began in 1532. This period of desta­bilization, or what Wachtel called “de structuration,” occurred several decades before the first comprehensive descriptions of the administrative system were written down in the Spanish chronicles and administrative documents.^[118] Although elements of the original system were in evidence in early and even mid-Colonial reports, nonetheless, major features of the administrative system and its recording apparatus had disappeared or become destabilized over the intervening years.

The circumstances outlined above complicate the task before us. The question is: How shall we proceed? In the first place, we do have a number of excellent secondary sources on these matters.^[120] These and other accounts inform us deeply with respect to the basic characteristics of Inka adminis­tration. While I will draw on material from these sources as a point of departure for the present study, I will do so primarily as a way of moving as quickly as possible to the aspect of that system I feel myself to be most qualified to comment on - cord-keeping. Having myself spent almost twenty years in close study of the corpus of extant khipus,^[121] it is my intention here to draw on data from the knotted-cord records in order to demonstrate how khipu accounts were constructed, maintained, and manipulated by the khipukamayuqs (knot-makers/organizers), the Inka record-keepers.^[122] In this way, I hope to produce an account of Inka administrative practice that is to some degree grounded in what I would term “indigenous testimony” - that is, native records produced in the course of Inka administrative practice.

In keeping with the desiderata and objectives outlined above, I will begin by presenting an overview of the basic institutions and practices of Inka administration. The intention in this initial section of the chapter will be to indicate the central principles and features of the Inka administrative system, as a basis for looking at the cord-records themselves.

An overview of Inka administration

In early Colonial sources, the Inka Empire is referred to as Tawantinsuyu, which we can gloss as “the four parts intimately bound together.” The four parts in question were Chinchaysuyu, Antisuyu, Collasuyu, and Cuntisuyu (the suffix -suyu [part, turn] is often glossed as “quarter”). At the heart of this quadripartite organization was the Inka capital city of Cuzco, located in the southeastern highlands of present-day Peru. The overview of the adminis­tration of Tawantinsuyu that follows is constructed top-down, as it were, beginning with administrative officials, institutions and procedures in Cuzco, moving down (and outward) to provincial administrative centers, and, finally, to local settlements. My objective is not to be exhaustive and/or definitive, but rather to provide a reasonably accurate overview from which to look more closely at khipu administrative record-keeping.

State/imperial organization in Cuzco, the capital

As the capital, Cuzco was the center of supreme power and authority in the Inka Empire. It was here that the Inka king - the Sapa Inka (unique/sole Inka) - reigned at court along with his Coya, the queen (who in late imperial times was his sister as well). The administration within Cuzco was staffed by direct and collateral descendants of the ten to twelve Inka kings who had ruled the empire during its short history, which lasted only some 125-150 years. Given the rapidity of state formation, it is not surprising that, while the administrative structure was reasonably well consolidated in the capital city, things were more in flux, with considerable local variation, in the provinces.

At the top of the administrative hierarchy in Cuzco and the empire stood the Inka. The indigenous chronicler Guaman Poma de Ayala details a number of officials who saw to the everyday needs and interests of the king.^[123] Most immediately, the Inka was attended to by a secretary (Yncap cimin quipococ, “he who carries the account of the words of the Inka”), a head accountant and treasurer (Tawantin Suyo runa quipoc Yncap, “he who carries the accounting of the people and goods of Tawantinsuyu”), as well as a counsel of four great lords, or Apus, each of whom was responsible to the Inka for the affairs in one or another of the four suyus of Tawantinsuyu. The Apus formed what Guaman Poma referred to as the Consejo Real, the “royal counsel,” a body that was served by a secretary, the Tawantin Suyo capac Yncacanap cimin quipococ (he who carries the words of the Inka and the lords/Apus). These were the principal authorities at the heart of what we could term “civil governance” in the Inka capital. However, we should not lose sight of the fact that what we classify as civil affairs, on the one hand, and religious affairs, on the other, were never far apart in Inka statecraft. Thus, we must include the chief priest, the Villac Umu, as well as the hierarchy of priests he oversaw, as players in the civil administration.

We must take note of an institution, the so-called ceque system, which provided the framework for administrative activities, social organization, and ritual practices in the city. The forty-one ceques that composed this system were (invisible) alignments of sacred places - called huacas - located in and immediately around the city. The huacas were sites where important events had occurred in the mythical foundation of the ancient capital. Each huaca received sacrificial offerings on a particular day of the year. Cuzco and the ceque system were divided into moieties (Hanan/upper Cuzco and Hurin/lower Cuzco), each of which was further subdivided into two parts, forming the four parts or quarters of Tawantinsuyu.

Figure 9.1 Schematic representation of the ceque system of Cusco showing division into upper and lower Cusco and the direction of hierarchical order of ceques in each half.

The performance of sacrifices at the some 328-350 huacas located along the forty-one ceques, plus an unnamed period of rest of thirty-seven days, structured the annual ritual calendar in the capital and empire as a whole. What made this ritual/calendrical system political, and, therefore, of rele­vance for a discussion of state administration, was the fact that specific royal and non-royal kin groups - called, respectively, panacas and ayllus - were responsible for making the sacrificial offerings at the huacas aligned along particular ceques. That is, specific sectors of the terrain in and around the city, as well as specific segments of time in the annual calendar, were related to one or another of the ten panacas or the ten ayllus into which the population was divided.^[124] Information pertaining to the ceque system of the city of Cuzco is said to have been recorded on a khipu.

Khipu analog for a cord account in Cuzco

Without wishing to claim that we have identified anything so spectacular as a “ceque khipu,” nonetheless, we can see in an extant pair of khipu samples a cord structure and organization that could have accommodated the segmentary and hierarchical features as outlined above.^{[125] [126]} As we see in Figure 9.1, the ceque system was a four-part arrangement with two quarters in the upper/Hanan moiety and two in the lower/Hurin moiety. Except for the quarter of Cuntisuyu (that is, which had fourteen ceques), the suyus generally contained (three x three =) nine ceques. We saw above that the hierarchical categories collana/payan/cayao proceeded clockwise in upper/ Hanan Cuzco and counter-clockwise in lower/Hurin Cuzco. Now, we have identified a pair of khipus, currently in the Banco Central de la Reserva del Peril, in Lima, that reflects structural divisions and a hierarchical organiza­tion strikingly similar to the ceque system.

The two samples in question are part of a group of five khipus tied together in what I have termed a “linked set” (see Figure 9.2).¹¹ In the figure, the two samples we will focus on are labeled UR053B and UR053C. The samples in this linked set all share a particular organization of cords by color; that is, all five khipus display the repeating three-cord color pattern: white

10

II

Figure 9.2 Khipu UR053 (ATE3517, Banco de la Reserva del Peril [photograph by Gary Urton]) showing the locations of the matching pair UR053B and 53C.

(W) / either light reddish-brown (RL) or moderate reddish-brown (RB) / light brown (AB). Note that RL and RB may replace each other (that is, some cords are light reddish-brown, while others are moderate reddish- brown; however, the two hues are assumed here to have equal value in the three-color schemes of khipus 53B and 53C). Table 9.1 juxtaposes the tabular data that we have recorded from samples 53 C and 53B. In khipu 53C, the W/ RL or RB/AB color sequence is repeated across three-cord sets of pendant cords (the pendant cord numbers are given in the column on the far left) in the arrangement: 1-2-3 / 4-5-6 / etc.; however, in sample 53B, the W/RL or RB/AB sequence appears on sets composed of two pendant cords, the second of which carries a subsidiary cord (that is, 1-2-2s1 / 3-4-4s1). Thus, the likeness between these two samples in terms of the repeating color sequence belies a fundamental difference between them at the level of the number and arrangement of cords bearing those colors: pendant/pendant/ pendant vs. pendant/pendant/subsidiary. I suggest that what we see in these two samples is a three-term arrangement of categories that mimics the three-term collana/payan/cayao organization of hierarchical labels described above for the ceque system.

Next, as demonstrated by the arrangement of these two samples in Table 9.1, we see that, from pendant cord #11 of sample 53C and pendant cord #1 on sample 53B, the numerical values registered on respective cords shown across from each other are identical, or (generally) quite close in value. However, if these khipus were, in fact, meant to register the same (or similar) data, they must have done so in a way that classified that infor­mation in different structural terms, as we saw above that there is a basic difference between the two samples in terms of cord structure and the repetition of the three-color cord pattern. As we will see below, there is

Table 9.1 A pair of matching khipus (Banco Central de la Reserva del Peru)

KHIPU UR053C

Table 9.1 (cont.)

KHIPU UR053C

another feature by which we realize that these two samples are almost exact opposites of each other - we might say complementary opposites - precisely as the Hanan/Hurin moieties of Cuzco were complementary opposites (for example, clockwise vs. counter-clockwise hierarchical rankings).

If one looks at the second column in each set of data for khipus UR053C and 53B, one sees there the notation for how the pendant cords are attached to the main cord of the respective khipus. The two forms of attachment types (the details of which we do not need to go into here) are recorded as either “V” (= verso) or “R” (= recto). I would note that the direction of attaching subsidiary cords to pendant cords is not recorded on khipu UR053b (that is, the sample in which every third member of a three-member/cord group is a subsidiary). The subsidiaries are therefore labeled “U” (= Unre­corded). Now, the attachment types V and R are actually what we might call opposite sides of the same coin. That is, a cord attached V, as viewed from one side of a sample, will appear as an R attachment when the sample is viewed from the opposite side (and vice versa). What this means is that, while these two samples are, indeed, a “matching pair” in terms of numer­ical values knotted onto adjacent cords, the match is obtained only if one views sample UR053C from the V side of the khipu at the same time as one views sample UR053B from the R side. In fact, if one viewed the two samples from the same side (that is, either both in the V or the R position), the numerical values of adjacent cords would not align, or match, as they do when their attachment type is opposite, as shown in Table 9.1. Thus, the “pairing” of these samples, in terms of the sequencing of cord colors and values, is obtained only when the khipus are placed (and viewed) in oppos­ing orientations.

My argument is that the difference just described between the orientation of cord attachments on these two samples is like that between the two halves (moieties) of the ceque system of Cuzco in which the hierarchical categories (collana/payan/cayao) of the three-ceque sets in one half run in a clockwise direction, while those in the other half run in a counter-clockwise direction. Given that it has often been suggested that the ceque system was recorded on a khipu,^[127] the question has long been: How was such a complex organization of sections and categories recorded? My suggestion is that, in

Figure 9.3 Hypothetical construction comparing the organization of the ceque system of Cuzco and the matching khipu pair UR053B and 53C.

fact, the ceque system most likely was not recorded on a single khipu; rather, I suggest that it was most likely recorded on a pair of khipus - one for Hanan/upper Cuzco, the other for Hurin/lower Cuzco (see Figure 9.3). A pair of samples like UR053B and 53C, shown in Figure 9.2, could have comfortably accommodated the recording of information in an arrangement of paired halves composed of three-term labels in which the terms repeat in a clockwise direction in one half and a counter-clockwise direction in the other half. A khipu pair of the type discussed here would have provided the instruments for recording and regulating - that is, administering - political and ritual positions and relations in the ceque system of the capital.

Provincial organization

As we move outward from Cuzco and down the administrative hierarchy, we come to the overseers of each of the eighty or so provinces that made up the empire. Each province was overseen by a Tocricoc (“he who sees/ watches”), who was attended by a khipukamayuq. This official recorded information, especially statistical data, that pertained to the province, such as census and tribute records. It is at the provincial level that we encounter the question of the degree to which decimal organization obtained in the hierarchy and oversight of state workers. The latter relates to the decimal­based system of corvee labor in which tribute was levied on subject popula­tions in the form of a demand for labor time on state projects, such as the building and maintaining of roads, storehouses, bridges, etc.; the care and tending of lands belonging to the state and to the gods; and other tasks.^[128]

Throughout much of the empire, corvee laborers were organized in decimal groupings according to the principles of dualism and five-part organization (see Figure 9.4). That is, five groupings of ten (chunca) workers at the local level made up groups of fifty workers, which were paired with another group of the same size to make a group of 100 (pachaca) workers. As we see in Figure 9.4, moving up the hierarchy, the principles of pairing and five-part organization worked together repeatedly to produce ever larger groupings of workers, up to the level of groups of 10,000 (hunu) tribute laborers. At each level, headmen (called curacas) oversaw the activities of the workers. Cord-keepers (khipukamayuqs) were assigned to record data con­cerning member attendance and participation in work tasks assigned to that group by the state.^[129]

Recording data at the provincial level

A question that has been central to efforts to understand how Inka adminis­tration actually functioned, on the ground, concerns how information moved between adjacent levels of the decimal hierarchy. The gist of the problem is illustrated in Figure 9.4. In the decimal hierarchy, commands for labor, etc., from higher-level officials would be passed down the chain of command to lower-level officials. It is clear that such instructions - for example, send 100 workers to move the harvest into storehouses in Huanuco Pampa - would be transmitted via khipu accounts. This information would have been partible in nature; that is, assignments made to 100 tribute payers would be broken down between instructions to two groups of fifty, and, in turn, from there to on-the-ground instructions to the five groups of ten workers within a local community. In the reverse direction, accountants in local communities would pass data on tasks performed by decimally organized work groups upward through the hierarchical chain of officials. In the latter instance, information at

Inka Decimal Administration

Figure 9.4 Schematic hierarchial organization of one suyu (quadrant) of the Inka decimal administration.

Hierarchy of matching khipu in puruchuco

Figure 9.5 Schematic arrangement of the Puruchuco accounting hierarchy.

each level would represent the summation of accounts from the level immedi­ately below. These accumulating data would eventually arrive in the hands of state accountants in Cuzco, where the highest level of accounting went on.

Only in very recent times have we identified a set of khipus linked hierarchically in the kind of reciprocal relationship of summation/partition that would have been characteristic of administrative accounting at the provincial level in the Inka Empire, as described above. As my colleague, Carrie Brezine, and I have shown, we see in a set of seven khipus from the site of Puruchuco, in the Rimac Valley, what we have termed an “account­ing hierarchy” whose organization is strikingly similar to that outlined above (that is, summation upward; division downward). The Puruchuco accounting hierarchy (Figure 9.5) also contains elements of “checks and balances,” whereby Inka accountants could ensure for themselves the ver­acity and trustworthiness of state records. The operation of this arrange­ment of khipus is too detailed to explain in full in the present context.^[130]

Basically, there are two principles at work in this accounting hierarchy: (a) khipus on the same level are “matching khipus” (that is, as we saw in Table 9.1); and (b) sums of groups of numerical values in different color- coded segments of khipus on lower levels are recorded on similarly color- coded segments of khipus on the next higher level. Thus, sums are being recorded “upward” (or, reciprocally, they are being sub-divided “down­ward”) in the Puruchuco accounting hierarchy. Suffice it to say that this example provides us with a clear and convincing case study of the produc­tion of accounts in the territory of a local lord - a senorio - and the communication by means of khipus between the lord and the provincial center to which he reported (in the case at hand this probably referred to an Inka administrative site lower down in the Rimac).

Local administrative organization

When we consider the administration of public affairs within local settle­ments, the offices of greatest importance, both in terms of practices of local control as well as in the relationship between the community and the outside, were a hierarchy of local lords, the curacas. These were the heads of the local lineages that made up what were usually multiple ayllus (kin­based, land-holding, ritual/ceremonial groups). The principal officials within such local hierarchies were commonly referred to in Spanish documents as cacique principal (the head of the most powerful lineage in the local area) and a close subordinate, the cacique, or segunda. Now, we should note that the principle of dual organization, which takes the form, in social contexts, of moieties (halves), was pervasive in communities throughout the Andes in Inka times (we have already seen an expression in Cuzco, the capital). Local moieties, which were usually hierarchically related to each other, were commonly referred to (or classified) as hanan (upper; the one that takes precedence) and hurin (lower; the subordinate group). In most local socio­political organizations, the moieties were made up of multiple ayllus, each headed by a curaca. The cacique principal was often drawn from a lineage of the predominant ayllu of Hanansaya, while the segunda represented the ayllus of Hurinsaya. This pyramidal, hierarchical arrangement of local curaca officials was generally structured and organized as shown in Figure 9.6,

Richard Burger, Craig Morris, and Ramiro Matos (eds.), Variations in the Expression of Inka Power (Washington, D.C.: Dumbarton Oaks, 2007), pp. 357-84.

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Figure 9.6 Dual, hierarchical organization of authorities in the Chicama Valley, 1565 (after P. Netherly, “The Management of Late Andean Irrigation Systems on the North Coast of Peru,” American Antiquity 29 [1984], 234).

which is an example drawn from ethnohistorical documents from the Chicama Valley, on the north coast of Peru, after Spanish contact.

In terms of our interest here in administration and record-keeping, I should note that the head officials of the moieties were served by khipu- kamayuqs - that is, there was a pair of local cord-keepers, one for the Hanansaya ayllus, another for the Hurinsaya ayllus. We find suggestions in the early Spanish administrative documents to the effect that this pair of moiety-based local cord-keepers not only maintained the records of their constituent ayllus, but that each retained a copy of the information pertain­ing to the opposite moiety, as well (thus, each moiety cord-keeper would have retained a record of all information, especially demographic, pertaining to the community as a whole). As a result of this form of what I have characterized elsewhere as a system of checks and balances,^[131] there were, at a minimum, at least two copies of all the records pertaining to any given local population. We now have solid evidence for such configurations of khipu samples in the extant corpus; one example, discussed in the previous section, is from Puruchuco, on the coast; the other example is from

Chachapoyas,^[132] in the north-central highlands of Peru. We also see evidence of this organization in the account of a visita (census visitation) among the Lupaqa, who lived on the southwestern shores of Lake Titicaca, in early Colonial times. In testimony from a local cacique, don Martin Cusi, of the sector of Lurinsaya (= Hurinsaya), we read:

It was asked if among the quipos, which in the other declaration it was said he had in his house, if he had found the quipo of the Indian tributaries they made in the time of the Inka in this province and that there were so many Indians, he said that he discovered the said quipo and then he exhibited certain cords of wool with some knots that was said to be the quipo and account of the tributary Indians that there had been in this province in the time of the Inka, the said quipo which the said don Martin Cusi and Lope Martin Ninara, who is the head quipocamayo of the said parcialidad [moiety] of Lurinsaya within the province, who is the person who has the account and explanation, as the accountant of the business [negocios] of the community they declared, and his declaration was made conferring part-by- part [in his reading] with the declaration made by don Martin Cari cacique principal of the moiety of Anansaya, the said person by his quipo, and it conforms in all sections and in the number of Indians of all the pueblos in both moieties except that in one part, that of the Canas Indians of the pueblo of Pomata, that [quipo] of don Martin Cari said they had 20 Indians and that [quipo] of don Martin Cusi and his quipocamayo by his quipo it appeared to be 22; in all other parts the declarations of the said caciques conformed.^[133]

This account gives us a sense both of the hierarchical arrangement of record-keepers as well as indicating the importance of checks and balances in the administrative accounting of local, moiety-based cord-keepers.

A local khipu: numeration, rank, and value in a khipu from Nazca

The question that concerns us now is: How might khipu accounts have been organized to record information (on census, tribute, and so on) that was vital to the organization of local communities in Tawantinsuyu? Asking this question, we are indeed “on the ground,” as it were, at the point where local information was collected, with all the messiness of political relations and

Figure 9.7 Khipu UR028 (Museum fur Volkerkunde, Munich; s/n C; photograph by Gary Urton).

other factors local cord-keepers would have had to contend with. To address the question of how administrative information may have been gathered, synthesized, and recorded on cord accounts at a local level, I turn to the analysis of an important and highly complex sample, which is in the collec­tions of the Museum fur Volkerkunde, in Munich, Germany. The sample in question, which I will refer to here as UR28 (see Figure 9.7), is one of six samples tied together into what I term a “linked set.” This set of samples was reportedly recovered from “grave robbers” (huaqueros) at Atarco, near Nazca, on the south coast of Peru. While some of the physical characteristics and organizational features that I will describe for UR28 are found in one or more of the other five samples in this linked set, I have space here only to discuss the one sample identified above.^[134]

Sample UR28 is composed of seventy-four pendant cords made of final S-ply cotton threads. A dozen of the pendant cords bear one subsidiary cord each. The cords of UR28 are either light brown (AB) or medium brown (MB). At the most general level, this khipu is organized into three sections as defined by the following cord groupings: (ι) cord #1, (2) cords #2-4, and (3) cords #5-74. The reader may follow my discussion of the organization of this khipu by viewing Figure 9.8.

Figure 9.8 is organized into three major sets of columns, as defined above, which are labeled (A), (B), (C). The left-most sub-column within each major set of columns shows the cord numbers, from #1 to #74 (the notation si that follows fourteen of the cords indicates a subsidiary attached to that cord). The next sub-column to the right (that is, within each major column set) shows the color of the cord, predominantly either AB or MB (several of the si cords in the lower part of the chart are color KB = “dark brown”). The next column to the right of the color notations displays the numerical values knotted into the respective cords. And finally, the right-most sub-column (appearing only in major column sets A and C) displays the sums of values recorded on groupings of cords in the sub-column(s) to the left.

What we find when we examine the organization of numerical and color values on sample UR28 is an arrangement that I would characterize as either the summation of set values from left to right and from bottom to top, or repartition (or subdivision) of set values from the top to the bottom and from right to left. That is, as we see, cord #i, an AB colored cord, carries the value 102; this same numerical value is the sum of the values knotted into cords #2-4 and their subsidiaries. The actual sums on the cord/subsidiary pairs of cords #2-4 are: 29/14,13/10, and 12/24 (= 102). Note that the pendant cords are color AB, while the subsidiaries are color MB. What follows, in cords #5-74, is a complicated arrangement of various groupings of five-cord sets; some of these sets are what I would term “odd” five-cord sets, in that the cord number of the first cord of each of these five-cord sets is a value ending in 5 (that is, 5+15+25; 35+45; and 55+65). The cords of these “odd” type five- cord sets are all AB (light brown). In addition, there are what I term “even” five-cord sets; that is, ones the first cord of which has a cord number that is

104

Figure 9.8 Schematic diagram showing the organization of cords, colors, and numerical values in Khipu UR028.

an even decimal value, ending in o (that is, 10+20+30; 40+50; and 60+70). The cords of these “even” five-cord sets are all MB (medium brown).

Now, when we sum the values on the “odd” and “even” groupings of five-cord sets, as those groupings are defined above, we find that, with one exception (see below), the sums are equivalent to those appearing on either the pendant cords or the subsidiaries in cord positions #2-4. Specifically, the “odd”/AB five-cord set sums are equivalent to the values on pendant cords #2, 3, and 4, while the “even”/MB five-cord set sums are equivalent to the values on the subsidiaries of the above three cords (that is, #2si, 3sι, and 4sι). It is clear that there is a recording error either on cord #4 (= 12) or on the two “odd” five-cord sets (55-9)+(65-9), which totals 14. I strongly suspect that the error is on the latter cord groupings, and that the intended sum of this latter pairing of “odd” five-cord sets should be 12 (as on cord #4), rather than 14. If we accept this explanation for where the error lies, we then note that the value 102, which is registered both on cord #1 and as the sum of values on cords #2-4, is replicated on the complex of “odd”/AB and “even”/MB five-cord groupings from cord #5 to cord #74.

In sum, khipu sample UR28 is a complex arrangement of bi-color (AB/ MB) cords organized in different arrays of “odd”/“even” five-cord groupings whose numerical sum (i02) is reproduced both on the cords and subsidiaries from cord #2-4, as well as on the first cord of this sample, #1. What can we surmise, or theorize, about what the use and significance of this khipu account might have been?

The first observation I would offer is that the numerical values registered on the five-cord sets strike me as similar in magnitude (that is, in the range 1-6, with an emphasis on the lower end of that range) to what I argued in an earlier paper²⁰ were census-type numerical values, particularly when what is displayed is not total household composition, but, rather, the number(s) of tributaries per household. In the case of khipu UR28, we could be looking at the count of tributaries within a number of ayllus, the clan-like social groupings. Specifically, I would interpret the six values on cords #2-4 and their subsidiaries (that is, the values 29/i4, i3/i0, and i2/24) as the tributary counts for six ayllu-like social groups in the area of Nazca. The total summary count, i02, is interesting in regard to census values, as well.

Gary Urton, “Censos registrados de cordeles con 'Amarres': padrones problacionales pre-Hispanicos y colonials tempranos en los Khipus Inka,” Revista Andina 42 (2006), 153-96.

Numerous Colonial Spanish sources^[135] inform us that one of the principal groupings used to organize populations in the Inka state census was the pachaca (one-hundred), a group composed of ιoo tributary (that is, corvee) laborers.

The above interpretation leaves us with the question of what could have been the meaning, or the sociopolitical organizational significance, of what appears to be a division of this (hypothetical) pachaca-sized census unit into two parts. This division is most apparent in the color difference between cords (that is, AB vs. MB) and in the distinction between odd and even five- cord sets. I would argue that here we are seeing the signing values used to identify a two-part moiety division of the pachaca. As we have seen, such dual groupings were exceedingly common in the Inka state. In most such instances, the two hierarchically related parts were referred to as Hanansaya (upper part) and Hurinsaya (lower part). I suggest that such a two-part sociopolitical moiety division was signed in khipu UR28 in three ways: (a) by color (AB/MB), (b) by the distinction between pendant cords vs. subsidiary cords, at cord positions #2-4, and (c) by the distinction between odd and even five-cord sets, at cord positions #5-74. In sum, I would argue that Figure 9.8 is a schematic representation of the moiety organization of six ayllus at Atarco, near Nazca, whose census was recorded on UR28.

It is interesting to note that the above interpretation may help explain why the summary cord (#1) in this sample is colored AB, rather than MB. That is, this would be explained on the principle of “encompassment,”^[136] by which the dominant member of a ranked, asymmetrical pair stands for the two parts when they are represented as a single unit. Thus, when AB and MB are brought together within a single unit, the identity of that single unit is signed by the color identity of the dominant member of the pair - in this case, AB.

To the extent that the above interpretation of the numbers, colors, and odd/even distinctions among cord groups in sample UR28 might have combined to detail the organization and status relations among a group of six ayllus divided into moieties (as outlined in Figure 9.8), we could con­clude that this khipu represents an instance of the organization of infor­mation by way of the linkage of signs for the numerical values and social types, or ethnocategories, making up a local population. Khipu UR28 represents the organization of local administrative information in an expli­citly social register.

Summary and conclusions

We began this chapter by viewing a quotation from the chronicle of Cieza de Leon, in which he commented on the extraordinary efficiency and accuracy of the cord-recording system of the Inka Empire, the khipu. We asked the question at the beginning of this study of whether or not, in studying extant samples in collections around the world, we could find evidence that would confirm Cieza's observations on the accuracy and efficiency of Inka cord­keeping. I believe we have succeeded in demonstrating complexity in Inka administrative accounting from the level of state accounting (in the ceque system) in the capital, in provincial accounting (in the Puruchuco accounting hierarchy), and in local accounting (in the khipu sample from Atarco, Nazca).

The various examples discussed in this study suggest several features of khipu-based administrative accounting. First, khipu records employed the full range of structural and visual variability that characterizes these devices (for example, cord and knot construction, attachment, color, grouping of cords by spacing and color). Second, there is no particular form of encoding used in any one of our samples that seems to be beyond, or radically at odds with, that found on the other samples. This suggests that there was a relatively high degree of conventionality of cord manipulation from the bottom to the top of the administrative/recording hierarchy. And third, in its structural and organizational properties, the khipu appears to have been perfectly suited to recording information deriving from sociopolitical struc­tures grounded in complementary dual organization and hierarchical seg­mentary organization. In short, the khipu was perfectly adapted to the encoding of administrative information in the Inka state.

It is to be hoped that future studies will direct additional light onto the practices, technologies, and systems of knowledge that sustained this extraordinary system of three-dimensional, cord-based accounting of ancient South America.

FURTHER READINGS

Bauer, Brian S., Ancient Cuzco: Heartland of the Inca, Austin: University of Texas Press, 2004. Brundage, Burr Cartwright, Lords of Cuzco: A History and Description of the Inca People in Their Final Days, Norman: University of Oklahoma Press, 1967.

Covey, R. Alan, How the Incas Built Their Heartland: State Formation and the Innovation of Imperial Strategies in the Sacred Valley, Peru, Ann Arbor: University of Michigan Press, 2006.

“Inka Administration of the Far South Coast of Peru,” Latin American Antiquity ιι (2000), 119-38.

D'Altroy, Terence N., The Incas, Malden, MA: Blackwell Publishers, 2002.

Provincial Power in the Inka Empire, Washington, D.C.: Smithsonian Institution Press, 1992.

Julien, Catherine J., “Inca Decimal Administration in the Lake Titicaca Region,” in George C. Collier, Renato I. Rosaldo, and John D. Wirth (eds.), The Inca and Aztec States, 1400-1800: Anthropology and History, New York: Academic Press, 1982, pp. 119-51.

Malpass, Michael A., Provincial Inca: Archaeological and Ethnohistorical Assessment of the Impact of the Inca State, Iowa City: University of Iowa Press, 1993.

McEwan, Gordon, The Incas: New Perspectives, New York: W.W. Norton & Company, 2006.

Morris, Craig, and Adriana von Hagen, The Incas, London: Thames & Hudson, Ltd., 2011. Silverblatt, Irene, “Imperial Dilemmas, the Politics of Kinship, and Inca Reconstructions of History,” Comparative Studies in Society and History 30 (1988), 83-102.

Von Hagen, Adriana, and Craig Morris, The Cities of the Ancient Andes, New York: Thames & Hudson, Ltd., 1998.