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Inka Khipu
Problems and Approaches

Alexandre Tokovinine
Anthropology Department
(Archaeology Wing)
GSAS, Harvard University
April 2003

 

Introduction

Despite a significant progress in the decipherment of pre-Columbian scripts over the past decade, of which the breakthrough in reading Maya text was the most spectacular, the writing system of Tawantisuyu remains a major puzzle. It seems, however, that the researchers in the field are getting closer to cracking the code of the Inca string-and-knot records. By now, only quantitative aspect of the khipu content is understood. Recent publications (Quilter and Urton 2002; Urton in press) indicate a shift to the new approaches, which may allow to go beyond the numeric values, as it once happened with the research on the Maya script.

Why has the decipherment of the khipu proved to be so challenging? Apart from the cases of such undeciphered scripts as Isthmian (Epi-Olmec), Easter Island, or Indus valley writing systems, when the researchers face the problem of the unknown language affiliation, insufficiency of the available material (texts are too few or too short, or both), and lack of secure cultural context, the Inka khipu are provided with a considerable cultural (social) and linguistic background. Therefore, the greatest difficulty in deciphering the Inka writing is in understanding the functional properties of the script, which is the only known complex writing system of non-graphic nature.

The goal of this paper is to present an overview of the current approaches to the study of the Inka khipu, as well as to reflect on the perspectives of the future research. I will start with a general description of the khipu recording devices. Then, I will proceed to the interpretations, which have been proposed so far. My next step will be to consider the colonial evidence on the nature of the khipu writing system. A forth stage will be to discuss the indirect evidence on the informational capacity and functional properties of the khipu devices. I will try to compare my observations with what I know about the two major writing systems of pre-Columbian America, those of the Aztecs and the Maya. Finally, I will attempt to formulate a general approach to the study of khipu and apply it to a particular case.

 

What is khipu?

Khipu is a recording device, organized by means colored cords (strings) and knots. According to first systematic description of the khipu provided by Locke (Locke 1923: 13-15), a typical khipu would consist of a primary cord of variable length, single or grouped pendant strings attached to the primary cord (sometimes with a top string), subsidiary cords attached to the pendant strings (Fig. 1a), and three types of knots (single knots for values above 10, long knot for 2-9, and a figure eight knot for the value of 1) tied on the pendant strings and arranged in a decimal positional system, so that the knots of lower values are located further from the primary cord. This description was later refined to include a dangle end cord a special string attached to the end of the primary cord (Ascher and Ascher 1981: 17). Blank spaces in the positional numeration were identified as zero values (Ascher and Ascher 1981: 30). Finally, some khipu were reported to have their primary cord equipped with tassels or/and ending in a large needlework bundle with a distinct ornament (Urton in press: 5; Conklin 2002: 65).

However, a descriptive definition of the khipu does not reflect the multiplicity of choices involved in the production of the knot-and-string records. This is why recent definitions of the khipu center on its chaîne opératoire. Thus, Aschers describe the following sequence of the production steps: (1) preparing individual cords (choosing the material, spinning the yarn, twisting the doubled strings of desired colors); (2) attaching the strings to the one that serves as a main cord and sometimes also to the grouping top cord; (3) adding a dangle end cord; (4) knotting the entirely prepared blank khipu (Ascher and Ascher 1981: 15-21). The scholars emphasize the distinction between the third and the fourth stages and illustrate it with the known examples of the not-yet-knotted blank khipu (Ascher and Ascher 1981: 21-23; Pl. 2.1-2.3). Conklin provides another stage-based description (Conklin 2002: 59-78). It includes such additional aspects as the posture of the quipucamayu (therefore, the direction of data recording and data retrieval), the choice of S-plied or Z-plied cord (Fig. 1b), the distinction between variegated, monochromatic, and bichrome plying programs (Fig. 2), front and reverse pendant string attachment (Fig. 1c), and two types of each kind of knots (Conklin 2002: Fig. 3.5, 3.11, 3.15, 3.23, 3.25-29).

Figure 2: construction of khipu cords by doubled (variegated effect) and interlocked (barber pole effect) replying

Figure 2: construction of khipu cords
by doubled (variegated effect)
and interlocked
(barber pole effect) replying

Several properties of the khipu organization are of crucial importance. First, the khipu are three-dimensional devices that can be visualized, but also touched. Second, as Aschers have pointed out (Ascher and Ascher 1981: 17-18, 62), the khipu can be assigned horizontal and vertical directions. There is also an initial hierarchy of cords (primary, top, and secondary). In other words, by means of vertical and horizontal arrangements of the strings, a khipu can transmit some structured data. Finally, the construction of a khipu involves other multiple and binary choices that may also affect the transmitted data.

 

Interpretations and Approaches

Below, I will consider and evaluate three different approaches to the decipherment of the khipu system. Lockes skeptical view deprives the khipu of any conventionalized value except numeric. Aschers approach emphasize the numeric and structural properties of the khipu as being able to convey complex mathematical concept, which may have been related to formalized narratives or government arithmetic. Finally, Urtons interpretation relies more heavily on the ethnographic and linguistic data and on the assumption that the content of the khipu is much closer to the Quechua language and worldview, than to some abstract mathematical ideas. However, these interpretations and approaches do not offer any decipherment of the script, but rather provide clues for further research.

Some general observations on the khipu decipherment provided by Quilter (Quilter 2002) could serve as a general introduction to the problem of the approaches and the methods. Quilters interpretation favors cross-cultural comparisons, notably, that between the khipu and the Ubeid tokens (Quilter 2002: 213-218). He notices that the institute of messengers indicates high level of conventionalization of the khipu records used as letters (Quilter 2002: 211). Quilter also argues that the presence of a formalized oral tradition does not necessarily mean that this tradition substituted writing (Quilter 2002: 209). Another interesting idea is that most successful writing systems are characterized by considerable internal diversity, redundancy, and arbitrariness as long as these negative properties allow the scripts to work well enough for the purposes to which they were intended (Quilter 2002: 219-220). Therefore, there is no ideal script, but there are many, which work.

The initial approach of the scholars to the khipu records was rather skeptical. Having identified the positional numeric component of the khipu, Locke was not sure if other components, of which he could identify only cord colors, had any conventional value (Locke 1923: 15). He suggested that the quipucamayus could use a scheme of roughly suggestive colors lacking the certainty of meaning and the minimum quantity of signs required of any conventional writing system of pictographic, ideographic, phonetic, or alphabetic nature (Locke 1923: 32).

This simplified vision of the khipu system did not satisfy Marcia and Robert Ascher offered a much more sophisticated interpretation of the knot-and-string records. Their observations were based on a sample of almost two hundred khipu (for example, Locke reviewed only 42 khipu). Moreover, Aschers suggested to analyze the khipu in a wider context of social, cultural, and symbolic structures characterized by some patterns of similarity that the researchers identified as cultural insistence a term borrowed from the lectures by Gertrude Stern (Ascher and Ascher 1981: 37-39). The Inka insistence encompassed cotton and wool cloth, portability, methodical, concern for special arrangement, symmetry, conservative, and fit (Ascher and Ascher 1981: 56).

Aschers approach is focused on the possible structures of the data encoded in the khipu. The key concept is that of the format that encodes the structure of the information before the actual data is fixed in the form of knots (Ascher and Ascher 1981: 81; Ascher 2002a: 91). Another important notion is the distinction between the numbers as magnitudes and the numbers as labels (Ascher 2002a: 87). Only specific formatting of the data defines the meaning of the labels in each individual case (Ascher and Ascher 1981: 32, 75; Ascher 2002a: 88-94, 101). The scholars pay special attention to the sets of khipu, which are conceptually related, either through similar structures or through shared numerological data (Ascher and Ascher 1981: 71-72, 118-120). Their observation is that cross categorization with categorical summation is present on some 25 percent of the khipu (Ascher and Ascher 1981: 89). The logical structures of the khipu turns out to be characterized by specific patterning and hierarchy constructed by means of course, cord placement, color coding, and number representation (Ascher and Ascher 1981: 109, 116-120). Color coding is described as largely arbitrary, flexible, and reinforcing the logical structures of the khipu (Ascher and Ascher 1981: 18-21, 61, 89, 121). Therefore, Aschers suggest that although some formats could represent narrative structures (Ascher and Ascher 1981: 75-76; Ascher 2002b: 111-112), the khipu were a logico-numeric system used to solve mathematical problems of variable complexity and nature (Ascher and Ascher 1981: 133-152; 158-166; Ascher 2002a: 101). Moreover, as flexible as it was, the khipu system, in their opinion, could not have a single set of shared meanings (Ascher 2002b: 106).

The idea of khipu as flexible structures received an interesting elaboration in the works of Frank Salomon who did field research in a modern Peruvian community, San Andres de Tupicocha in Huarochiri Province, and studied the usage of khipu in the context of the ayllu-based social organization (Salomon 2002). Salomon suggests that the structures of these particular khipu consisted of discrete blocks of information encoded with colored strings, which corresponded to the social and economic units operated by the ayllu president and could be rearranged as some sort of game boards with subsequent calculation procedures (Salomon 2002: 308-311). Salomon directly compares these movable blocks with a deck of cards or with Mesopotamian tokens (314-315).

Although Salomon acknowledges himself that his concept cannot be applied to most Inka khipu (Salomon 2002: 310), the idea of the format as being casually manipulated, undermines that beautiful vision of the structured records proposed by Aschers. Once the format becomes subject to the constant change, the colored strings remain the only conventionalized units. However, within the logic of the Aschers system, the format assigns values to the cords.

An even more elaborate and comprehensive interpretation of the knot-and-string devices has been recently proposed by Gary Urton. He distinguishes between the statistical khipu and the so-called anomalous ones, which constitute one third of the total known sample and may contain narrative accounts (Urton 2002b: 183-192; Urton in press: 53-55)1. Urton suggests that the khipu system is structured as a binary code and therefore consists of units of information that take the form of strings of signs or signals, each individual unit of which represents one or the other pair of alternative (usually opposite) identities or states (Urton in press: 1). One major argument is that the stages in the khipu chaîne opératoire were all binary in nature (Urton in press: 37-39). Another important point is that the practice of interfacing arrays of stones in reading khipu accounts is well attested in the historical literature Urton suggests that the stones could have been laid out as a record of the sequence of binary decisions (Urton in press: 43, 125-129).

The signifying unit is a single knot identified as a token or the object used as a clue to some other object or event in the past (Urton in press: 141-142). For the case of the anomalous khipu like B/8705, Urton suggests that the subunits on the strings could be some form of logographs with conventionalized word/morpheme-level values (Urton in press: 98-102). He compares the khipu with the Mesopotamian token-based and early graphical systems, where there were some structured logographic signs with the syntactic relationships underrepresented due to the obvious context and format of the messages (Urton in press: 15-17).

According to Urton, the sequence of the decision-making events for each binary coded sign would include seven steps: (1) choosing either cotton or wool to spin the strings; (2) choosing one of the two color classes; (3) spinning the string in either Z-spun/S-plied or S-spun/Z-plied pattern; (4) attaching the string to the primary cord in either recto or verso version; (5) knotting the string in either decimal or non-decimal pattern; (6) tying the knot in either Z or S pattern; (7) tying the knot to register either even or odd number (Urton in press: 119-121).

Urton relies on the concept of insistence proposed by Aschers, as well as on Bourdieus theory of habitus. He argues that the binary oppositions or dual structures form an essential part of the Inka cultural reality (Urton in press: 43-45). Thus, the symbolic dualism is expressed in the Inka numeric system characterized by the opposition of odd (chulla) and even (chullantin) numbers (Urton in press: 89-90). Another opposition, the binary organization of colors, is attested among the modern Quechua speakers in Central Bolivia who classify the dyed thread colors into two rainbows (Urton in press: 104-111). The social dualism is represented by the moiety organization (Urton in press: 149).

Urton also introduces the theory of markedness in order to look for parallels between complementary and hierarchically related pairs of terms in the Quechua worldview and in the khipu records (Urton in press: 45-47). Therefore, even-odd, red-dark, S/Z binary oppositions could have corresponded to some male/female, upper/lower, senior/junior complementary pairs of unmarked/marked categories, which are so pervasive in the Inka social and cultural world (Urton in press: 148-150).

Urtons approach is much more persuasive and it allows looking for some repeating patterns in the khipu in order to establish a relationship between the language of the khipu system and some units within the system. The markedness theory is especially significant. One can find some marked/unmarked categories or paired terms in the Spanish translations of the khipu accounts and look for similar patterns in the khipu themselves. The problem of the signifying units, however, remains partially unsolved. For example, if the numbers of a particular string are meaningful, then one cannot control their odd or even values. If only oddity and evenness matter, it is hard to explain why different odd and even numbers are used. Besides, there seems to be a break in the operation chain between the production of the strings and knotting, the latter phase leaving some room for combinations (sections, sequences of knots with different directionality) but within the given string format. Finally, Urton acknowledges that the binary code concept leaves the question of multiple color values largely unresolved (Urton in press: 131).

 

Khipu as described in the colonial sources

The path-breaking monograph by Locke already included an extensive collection of Spanish accounts on the khipu system (Lockes 1923: 33-84). Recent research has been concentrating on making sense out of the colonial references and on establishing some criteria in order to find most reliable sources. Thus, Urton distinguishes the sixteenth century accounts by Cieza de Leon, Sarmiento de Gamboa, and Cristobal de Molina from those by the chroniclers of the post-Tolledan period (Urton 2002a: 9-10). The latter was the time when the confrontation between the Indian records and the Spanish documents involved in the disputes over the property rights, the amount of tribute, and political authority prompted Spanish attempts to undermine the validity of the khipu accounts. The dispute over the right to monopolize the public records ended in 1583 when the Third Council of Lima condemned the khipu as idolatrous objects and ordered them to be burned (Urton 2002a: 10). However, the most extensive and valuable information about the khipu system was provided by the early seventeenth century chroniclers, especially Guaman Poma de Ayala, Garcilaso de la Vega, and Blas Valera (Urton 2002a: 11-14; Urton in press: 18; Assadourian 2002: 127-128).

There are three important questions about the khipu that the early colonial authors attempted to address: the social context of the Inka records, the types of the messages transmitted by the khipu, and the nature of the signifying units. The answers depended on the time when the accounts were written, as well as on their authors roles in the disputes about the validity of the khipu records for the colonial administration. For example, Blas Valeras investigations and writings had a clear agenda behind them, as he led a group of Jesuits of Spanish and Inka origin who attempted to assert the importance of the Inka cultural heritage including the khipu (Assadourian 2002: 127-128, 135; Hyland 2002: 153-154, 158-165).

Most Spanish authors agree upon the fact that the usage of the khipu was restricted to a particular class of officials. In Cristobal de Molinas words (as cited in Locke 1923: 36), they had expert Indians who were masters in the art of reading the quipus, and the knowledge was handed down from generation to generation, so that the smallest thing was not forgotten. Cieza de Leon and Jose de Acosta provide similar descriptions of the Inka literati (Locke 1923: 34, 37). Garcilaso de la Vega offers an even more exact definition: The knots or quipus were in the charge of special Indians called quipucamayu, meaning one who has charge of the accounts (Garcilaso de la Vega 1966: 331).

Guaman Poma mentions some high standing secretaries in the Inka imperial administration who were in charge of the overall records (Huaman Poma de Ayala 1978: 99-100, 101). However, most chroniclers focused on the role of the quipucamayus in the provincial administration. Thus, Cieza de Leon describes how the local statistical records were maintained and sent annually to the capital, as well as how the overseers inspected the provincial khipu and checked the balance of the accounts (Locke 1923: 35). Garcilaso even claims that there were several quipucamayus in each village in order to minimize accounting mistakes (Garcilaso de la Vega 1966: 331). Cristobal de Molina notices that the complex accounting system in the form of khipu was introduced with the large scale conquests during the reign of Inka Yupanque (Locke 1923: 36).

Most Spanish authors did not seem to be interested in the khipu accounts in the contexts other than census and tribute records. Their informants usually belonged to the provincial elite that dealt only with the conventionalized statistical khipu system imposed by the state administration. For instance, Cieza de Leons distinction between the oral narratives and the written statistics could well have been suggested by some local lord.2 Interestingly, we do know that his informant on the khipu was a provincial lord Guacarapora who continued to submit statistical data after the conquest, but to the Spanish authorities (Locke 1923: 34). According to Garcilazo de la Vega, the local khipu-keepers were also in charge of the historical records, which they combined with the tradition of memorized histories (Garcilaso de la Vega 1966: 332). He also cited Blas Valera who claimed to have found some proper historical knots (Garcilaso de la Vega 1966: 127).

Taking into account the context as well as some preferences of the chroniclers, we can better understand the information that they provide about the content of the khipu. For example, Cieza de Leon writes about military census, conscription, and the tribute assembled by the provincial authorities (Locke 1923: 34-35). However, some authors do mention a wider range of possible messages carried by the khipu. According to Cristobal de Molina, quipucamayus could record historical and calendric information (Locke 1923: 36). Jose de Acosta broadens the range to include laws and ceremonies (Locke 1923: 37). Finally, Garcilaso de la Vega states that any structured data could be recorded by means of a khipu, but complex data had to be packed into simple logical structures, which were in turn backed by the oral tradition.3 He is the only chronicler who really talks about structures and describes the process of archiving the speech into some conventional formats for both traditions, written and oral.

The nature of the signifying units was, of course, the hardest question for the chroniclers. Thus, Cieza de Leon only mentions the positional decimal organization of knots as numbers and concludes with saying that the Indians had no letters (Locke 1923: 34-31). Christobal de Molina already notices the role of color-coding, but his understanding does not go beyond comparing khipu with rosaries (Locke 1923: 36). Jose de Acosta was probably the first colonial author to distinguish explicitly between the known graphical writing systems including alphabetical ones and the system of the khipu: they of Peru had no kind of writing, either letters, characters, ciphers, or figures (emphasis is mine A. T.), like those of China and Mexico (as cited in Locke 1923: 37). He further elaborates his idea suggesting that the khipu could signify things by means of knots and diverse colors, as well as describing some mnemonic devices based on the colored stones that were also used by the Indians (Locke 1923: 37). Acostas definition is very similar to that proposed by Sarmiento de Gamboa: on these cords they make certain knots by which, and by differences of color, they distinguish and record each thing as by letters (Sarmiento de Gamboa 1999: 41). However, Sarmiento also mentions the oral tradition and some related historical boards displayed and stored in the Inka capital (Sarmiento de Gamboa 1999: 41-42, 200).

As in the case of the discussion of the variance in the khipu content, Garcilaso de la Vega offers an interpretation that somewhat stands apart. He underlies three major aspects of the khipu system numbers (knots), color-coding (strings), and logical structures (arrangements of the strings). In accordance with some earlier chroniclers and with what we know about khipu, Garcilaso de la Vega describes the numerical component as being a decimal-based positional system.4 As for the colored strings, he pays special attention to the fact that mixed color values had separate significances and that sometimes the combinations of three or more colors were used.5 Nevertheless, I think that the most interesting part of Gracilaso de la Vegas comments is about the structure. First, he mentions the main thread (a longer string like a fringe) as a primary element of the khipu internal organization (Garcilaso de la Vega 1966: 330). He also describes the subsidiary cords.6 Moreover, he goes on and claims that the non-numeric meaning could be entirely encoded through the structure representing conventionalized formats:

Objects that had no special colors were arranged in order, beginning with the most important and proceeding to the least, each after its kind, as cereals and vegetables (Garcilaso de la Vega 1966: 330)

Several examples of such classification-based format are provided including those of weapons and age-groups (Garcilaso de la Vega 1966: 330). However, according to Garcilazo, these structures could be manipulated to create some new formats and provide the knots and the colors with multiple meanings.7 I would speculate that this particular interpretation is really close to the concept of the khipu as a logico-numeric system.

It remains unclear if Garcilazo de la Vega had a chance to look at anything but statistical khipu. His inferences about the complex nature of the khipu devices and about the variety of messages carried through the string-and-knot record were likely based on the papers written by Blas Valera who did emphasize the intricate nature of the khipu devices:

The fables and verses, Padre Blas Valera says he found in the knots and beads of some ancient annals in threads of different colors: the Indian accountants in charge of the historical knots and beads told him the tradition of the verses and the fable (Garcilaso de la Vega 1966: 127)

As I have already mentioned, it was Valeras general attitude towards the Indian cultural legacy that might even have led to some pure speculations and inventions on his own part. Nevertheless, his complaint about the progress in understanding the khipu is quite relevant even today:

We moreover are slower in understanding their books than they in following ours; for we have been dealing with them for more than seventy years without ever learning the theory and rules of their knots and accounts, whereas they have very soon picked up not only our writing but also our figures, which is a proof of their great skill (quote in Garcilaso de la Vega 1966: 823-824)

In the same fragment, Blas Valera makes another important observation that seems to be in some accordance with what Garcilaso de la Vega described as different ways of structuring the data presented in the khipu:

The Indians are ingenious in memorizing with the aid of knots, the knuckles, and places; and they can moreover use the same knots for various themes and subjects, and when a subject is mentioned (emphasis is mine A. T.) they can read off the account as fast as a good reader reads a book, and no Spaniard has yet contrived to do this or to find how it is done (quote in Garcilaso de la Vega 1966: 824)

Therefore, the idea of some formats, which suggested meaning, seems to have appeared not only in the mind of Garcilaso de la Vega (of course, one can always speculate that he borrowed it from Blas Valera). The fact that the situation with understanding the khipu was complicated by multiple formats is confirmed by some late seventeenth century chroniclers. Thus, Bernabe de Cobo writes that even among the quipucamayus there was no shared way to read their khipu and that there were various types of the quipus for different sorts of things including tributes, lands, ceremonies, and negotiations (Cobo 1956: 143). I believe that Cobos passage can be understood only in the context of an earlier discussion about the different khipu formats: there were so many formats that most khipukamayuq knew only some of them. Moreover, he goes on to mention a remarkable episode when the lords of tambo de Cordoba managed to find the Indian who killed the Spaniard he was guiding one year after the crime. Some quipucamayus did it by means of consulting the khipu accounts in which presumably the day, the nature of the service, and the name of the guide were recorded (Cobo 1956: 144).

The greatest puzzle of the early colonial accounts is that despite a century of coexistence of the Spanish and the Indian written traditions, the latter remained largely beyond the European understanding. It seems that several factors were at work. First, the chroniclers dealt mostly with the Inka documents, which recorded statistical data. It could be the case that the set of conventionalized formats began falling apart right after the conquest, so that later chroniclers witnessed higher degrees of regionalization in the khipu accounting tradition. That process likely went along with the demise of the former lingua franca of the empire. According to Garcilaso de la Vega, Quechua was forgotten in many provinces, since there was no more benefit or necessity for the local elites to use it (Garcilazo de la Vega 1966: 403-404). The second factor was that the khipu writing system, presumably of logographic nature, differed markedly from the alphabetic script of the Spaniards. This issue was thoroughly analyzed by Gary Urton, especially in respect to Garcilasos account on the khipu (Urton 2002b: 178-184). There was also the problem of de-formatting the native documents into the structures, which would look more familiar to the Spanish eye. Nevertheless, the real problem is why, as Quilter puts it (Quilter 2002: 199), the Spaniards never really used or incorporated the statistical version of the khipu in the same way as they did with the census and tribute documents of the Aztecs. The puzzle is getting more complicated, as it becomes clear that the chroniclers were largely aware of the major components of the khipu writing system knots, colored strings, various formats, and some basic information packing procedures.

I would speculate that the answer to this question is not located in the dimension of the formal classifications of the writing systems, to which we are accustomed today. Of course, the inability of the sixteenth or seventeenth century Europeans to acknowledge that the true writing could be non-alphabetic should not be underestimated. Nevertheless, the most striking difference that the Spaniards could not overcome was between the whole experience of graphic writing systems and the only complex non-graphic system known so far. Moreover, the khipu script was grounded in the native tradition of complex fabrics and textiles that was also completely alien to the Spanish culture. Even those who wanted to understand the basics of the khipu simply could not grasp anything familiar enough, except the numeric knots. It is significant that we do not have any complete list of string values (even within a particular regional tradition) composed by a Spanish chronicler. There are only individual examples, as the total system obviously escaped the European mind.

 

Indirect evidence: structures, units, and informational capacity

Structures

Although the Spaniards could not read the khipu records themselves (despite all these claims in the chronicles), they had to deal with these documents being the principal source of information in the conquered empire. Khipu were translated and transcribed, especially in the context of the royal inspections (visitas) and the disputes between Colonial and Indian authorities over the amount and the nature of tribute. The significance of these early testimonies is hard to overestimate: they provide us with the information about the actual content of the khipu and about possible structures, into which that content could be organized.

In a recent paper devoted to the problem of the Spanish transcriptions of the khipu, Gary Urton underlines several methodological difficulties in dealing with this sort of accounts (Urton 1998: 412-413). First, the transcriptions represent only one kind of documents tribute records, so that it is hard to make any inferences about the content and structure of other formats of the khipu. Second, each transcription was a three-stage act involving some subsequent interpretations by a local khipukamayuq, a translator, and a Spanish scribe. Finally, the nature of the Inka tribute system did not correspond well to that of the Spanish. Urton centers on the contrast between the service-based Inka and the item-based Spanish scheme, to which the khipukamayuq had to adapt (Urton 1998: 421-428). He documents a shift from the rich in verbs narrative-like entries in the earlier accounts to the simple lists of tribute items in the later documents. According to an earlier observation made by Murra, the final imposition of the Spanish tribute in kind system happened in the late sixties of the sixteenth century, whereas the khipu transcribed in the late forties were still well within the Inka time-and-energy scheme (Murra 1982: 245, 252). Moreover, the khipukamayuq had to include additional categories of items those introduced or imposed by the Spaniards (Murra 1990: 54).

Earlier transcriptions of the khipu illustrate high degree of correspondence between the language structures and the way the data were encoded into the khipu. In the khipu fro Huanuco (Huanuco labor assignment) transcribed during the inspection of 1549, each cord corresponded to a complex sentence with main and dependent clauses (Julien 1982: 135-138; Urton 1998: 425-426; Murra 1982: 240-244). A distinct set of verbs was used in reference to different kinds of service or tribute (see Appendix, Table 1; Urton 1998: 426, Table 1). Urton notices, that the strings of another well-known document, the khipu from Xauxa, were transcribed as even more complex narrative passages involving multiple subordinate and independent clauses (Urton 1998: 427).

The content of later statistical khipu reveals some patterning of the information into discrete and hierarchically organized groups. Murra was the first to identify this patterning: he described it as ethno-categories (Murra 1990: 54). He also suggested that most categories could be reduced to a set of binary oppositions, especially to that of the raw and the cooked, which Murra interpreted in a broader context of domestic or private versus wild or state-owned (Murra 1990: 56). Both aspects of the transcribed khipu organization, the hierarchical sequencing of the data and the reduction of the content to some binary opposition, are of great importance for anyone who would try to break the code of the khipu. The observation by Gracilazo de la Vega that was mentioned earlier in this paper does support the point that the khipu not merely reflected the existing oppositions and hierarchies, but were structured along the ethno-categories.

Transferring the data into binary opposition could serve as an effective way to compress the information into fewer signifying units. I tried to check this hypothesis by pooling the lists of items and services based on the analysis of the transcribed khipu provided by several authors (Murra 1982; Julien 1982; Murra 1990). The results are given in the Table 2 (see the Appendix). Despite the fact that the provenience of the khipu is different, both geographically and chronologically, there is a considerable overlap between the categories. It is hard to say if the broad ethno-categories are present, but what I would call instrumental binary classifying is attested. For example, a khipuqamayuq in the Lupaca province could move through the sequence of binary choices and describe a particular way the fish was contributed as a tribute with only one sign and two diacritical markers (fish is dried or fresh and it is [sent] to Cuzco or not to Cuzco). Interestingly, these formatting decisions quite obviously depended on some local circumstances, so that the context of the khipu really mattered when reading it.

Of course, the functions of the khipu as an administrative tool were not limited to listing tribute. Names and place names must have been the second if not the primary content of the state records. Indeed, as it has been proposed by Zuidema, the famous ceque system of Cuzco described by Cobo looks suspiciously similar to a khipu, both in general layout and in its structural properties (Zudema 1982: 445-446, 451). Another interesting case is the khipu from Chachapoyas recently described by Urton (Urton 2001). Urton suggested that the latter khipu somehow integrated calendric and administrative data, as the number of the pendants corresponded to the number of days in two solar years, whereas the total numeric value of the knots roughly corresponded to the number of tribute payers in the area (Urton 2001: 140-144). This interpretation is extremely interesting, as it offers a very different picture of recording labor organization: day-by-day turn taking by a fixed number of tribute payers (strangely similar to the situation described by Salomon in a sense that the whole list becomes a set of socio-economic units, which can be arranged in variable order). If the individual strings of that khipu corresponded to a particular kind of tribute or service, the overall picture would be different from the transcripts of the khipu described above. Moreover, it would raise another interesting question also discussed by Urton but in an earlier paper the rationale behind the calculations, which were performed by the khipuqamayuq before the Spanish inspectors (Urton 1998: 417-420). I agree with the interpretation that it was some sort of authorizing gestures. However, I would speculate that this public calculation did not necessarily involve common denominators: probably, a khipuqamayuq had to demonstrate that the totals were really based on the day-by-day account so that the balance would not be questioned.

Units and information capacity

As I have already mentioned, the ambiguous nature of the khipu signifying units remains the major obstacle in any quest for its decipherment. I will suggest that the major component of the khipu signifying unit was a colored string. This idea is not new. Actually, this is suggested by most colonial authors, except the Jesuit group led by Blas Valera who argued for a more complicated phonetic system.

I think that the most significant argument in favor of my hypothesis is the context of the Inca records, or more precisely, the pre-Inka tradition of the khipu-like systems. The most distinct subset of the early string-and-knot devices are the so-called wrapped khipu, which are now securely identified with Huari culture (Conklin 1982: 267, 268; Radicati 1990: 44). Most of these khipu, however, have no provenience, including those described by Conklin (1982) and Radicati (1990). The striking feature of these khipu is the absence of the positional system, at least in its familiar form,8 and the summary cords (Conklin 1982: 271, 275-276; Radicati 1990: 43). Another specific trait is a complicated color-coding involving color combination at the level of spinning and plying (barber pole vs. variegated effect), as well as wrapping of the top potion of the cord (Conklin 1982: 275; Radicati 1990: 43). Secondary strings are inserted into the plaiting of the main cord before forming a cow hitch (Conklin 1982: 271). However, the overall structure is remarkably similar to that of the Inka khipu. It includes same overall form (actually, these khipu can also be stored in a spiral form), a hierarchy of cords, high redundancy of units, correlation between the organization of groups and the combinations of colors and knots, barber pole vs. variegated color mixing, cotton strings of natural colors, binary organization, as well as base five and base ten information sets (Conklin 1982: 274-278).

Another interesting piece of evidence comes from a colonial source. Of at least six pictures of khipu in the famous Nueva Coronica y Buen Gobierno by Felipe Guaman Poma de Ayala, there is only one depiction of knots (Fig. 3a). All the khipu look extremely uniform a primary cord and a series of subsidiary strings. I do not believe that this feature could be attributed to Guaman Pomas ignorance of the khipu. First, he does depict a calculating device in reference to one of the khipu. Second, and probably most important, he is extremely attentive to details, but when he does not have enough space, he draws only the most significant things. For example, his depictions of Spanish manuscripts usually contain real words (Fig. 4b). However, drawing a much smaller opened book (Fig. 4c), he leaves only imitations of words.

(a) Inka store (Guaman 1993: 253)

(a) Inka store
(Guaman 1993: 253)

(b) Inka treasurer (Guaman 1993: 272)

(b) Inka treasurer
(Guaman 1993: 272)

(c) Inka provincial administrator (Guaman 1993: 263)

(c) Inka provincial administrator
(Guaman 1993: 263)

(d) Inka youngster [as a messenger] (Guaman 1993: 150)

(d) Inka youngster
[as a messenger]
(Guaman 1993: 150)

Figure 3: representation of khipu by Guaman Poma

I suggest two interpretations. First, Guaman Pomas sketches of the khipu simply represent what he thought to be significant the primary cord, the secondary strings, but not the knots. Second, he drew messengers (Fig. 3d), administrators (Fig. 3c), treasurers (Fig. 3b), astrologers (Fig. 4a) who are holding khipu as an attribute of their profession but are not reading their khipu at that particular moment. By contrast, the accountant in the storehouse is actively interacting with the khipu in a similar way, as does the Spanish scribe writing a letter (Fig. 4b). A khipu without knots is a closed book and indeed, Guaman Poma draws both, a closed book and a knotless khipu when the two items are mere attributes of the person depicted (Fig. 4d).

(a) Inka astrologist and poet (Guaman 1993: 726)

(a) Inka astrologist and poet
(Guaman 1993: 726)

(b) Spanish scribe <br>(Guaman 1993: 405)

(b) Spanish scribe (Guaman 1993: 405)

(c) Spanish priest <br>(Guaman 1993: 506)

(c) Spanish priest (Guaman 1993: 506)

(d) Regidor with a book and a khipu (Guaman 1993: 654)

(d) Regidor with a book and a khipu
(Guaman 1993: 654)

Figure 4: representation of khipu and books by Guaman Poma (continued)

The colored strings alone have a considerable information capacity. The sum of single, double, and triple color combinations allows creating 252 unique signs. Moreover, we know that the barber pole versus variegated type of color mixing was introduced as early as Middle Horizon and that it is well attested for the Inka khipu (Conklin 2002: 63, 70-72, Fig. 3.21-3.23). This eventually doubles the amount of signs. Therefore, the colored string capacity was at least 504 unique values. Besides, the choice of recto/verso attachment to the main cord and S- or Z-plying pattern provides at least two levels of binary classification. My sample of tribute categories contains only 73 entries (Table 2). This is obviously far from the total list, but it seems that 504 basic verbs, nouns, and adjectives would be sufficient for most administrative purposes. For example, the formal vocabulary of most royal Maya inscriptions was about 300-400 words. The long calendric and maybe tribute or census-related khipu mentioned above (UR6) has only sixteen color combinations. Moreover, the system would not be closed, as the new types of signs could always be introduced through more complex color/plying combinations.

 

Writing, language, and some comparisons

There is no reason to doubt that Quechua was the language of the khipu. Moreover, it seems plausible to suggest that the system already existed before the rapid expansion of the Empire and the imposition of Quechua as a lingua franca over a mosaic of ethnic groups. However, Quechua did not achieve linguistic hegemony even in the immediate vicinity of Cuzco (Mannheim 1991: 43-52). Consequently, the Quechua-based khipu writing had to adapt to the growing complexity of the empire as a socio-political, economical, and linguistic system.

To what extent did the Inka khipu evolve in response to the challenge of incorporating new social categories, names of the peoples, places, and things? I will try to answer this question by comparing the khipu with another imperial writing system that of the Aztecs. There are several reasons why the latter seems to be a good comparative case. First, the language of the Aztec script, Nahuatl, is also agglutinative, so extra-long words containing several morphemes are common. Second, the Aztec scribes had to face similar problems: huge amount of foreign words (especially place names) had to be somehow incorporated into the script. Finally, early colonial scribes identified the vast majority of Aztec hieroglyphs, so the only problem for later researchers (apart from the situation with the khipu) was to understand how the system actually worked.

The Aztec response was an increased degree of phoneticism in the script. The latter, however, never lost its predominantly pictorial-logographic nature (Karttunen 1982: 398-399). Instead, the so-called rebus principle was introduced: the reading of a logograph, or part of it could stand for a phonetic sign. The rules of using logograms as phonetic signs had never been fully conventionalized. Thus, the reader had to determine himself whether a particular compound sign corresponded to a logogram, a set of syllabic signs, or something similar (Whittaker 1993: 13). The way that system worked can be illustrated with the logogram XOCHITL flower that appeared as a phonetic sign in the following combinations: MACUI(L)- XOCHI-TEPEC, MACUI-XOCHI(TL), XOCHI-MIL(CO), XOCHI-MIL-TZINCO, etc. (Fig. 5; Galarsa and Allain 1989: 92-97, Fig. 1-3). The borrowing into the system meant alteration of the original foreign word into some meaningful form (Whittaker 1993: 17).

Figure 5: words with XOCHI(TL) logogram (Galarsa and Allain 1989: 93, Fig. 1)

Figure 5: words with XOCHI(TL) logogram
(Galarsa and Allain 1989: 93, Fig. 1)

Of course, we should not dismiss the possibility, that the Inka khuipukamayuq could invent an entirely new set of phonetic signs. The canonical syllable structure of the Quechua language is CV(C) with a glottal catch for phonemically vowel-initial words (Mannheim 1993: 122). Therefore, it would be relatively easy to compose a syllabary. Moreover, there is a curious set of abnormal khipu with knots, which do not seem to have standard numeric values and could have been either logograms, or syllabic signs.

Urton recently described one such unusual khipu (B/8705; Urton 2002b: 184-191). The most remarkable aspect of its structure is that each subsidiary string bears three or four clusters of knots, which include the abnormal long knots with values above nine and some single knots, which appear in the same decimal positions as the abnormal long knots. As a result, the standard numeric layout is completely skewed. Interestingly, despite the generally atypical Z-span, the colors and the S/Z patterns do not seem to play any major role in this khipu. Urton suggested that the threefold structure could correspond to some logographic elements (Urton in press: 102). Then, the khipu must be a list of name or toponyms, because these sequences repeat only three times out of ninety-six. Another possibility is that the clusters of single knots and the abnormal knots correspond to syllabic signs in what seems to be a piece of poetry. However, it would restrict the total syllabary to some 28 signs (19 variants of long knots and 9 variants of the clusters of single knots). Even given the conservative estimation of the number of consonants, a speaker of Common Southern Peruvian Quechua would inevitably run out of signs (Mannheim 1993: 122-123).

By contrast, some patterns of color change do recall the rebus writing of the Nahuatl speakers. Sometimes the strings of two colors are combined in neither barber pole nor variegated way: the cords are simply joined instead (Fig. 6; Urton in press: 105-106, Fig. 4.10). The insertion of a brightly colored woolen string might have served a same function.

 

Some concluding remarks

Khipu is a complex writing system based on a set of conventionalized signs and some practices of formatting the information using the conventionalized signs as token. In my opinion, colored strings are the most likely candidates for the conventionalized part of the system. They likely corresponded to some words in Quechua. The binary choices in categorical ordering of the information and on the each stage of the khipus chaîne opératoire provided the formatting tools. Therefore, the system was characterized by high flexibility. The cost, however, was that potentially not all the khipukamayuq could easily read the messages of their colleagues.

Although the colonial chroniclers did not understand the khipu system, their descriptions of its content, functions, and social context are highly valuable. It is important that the chroniclers asked the same questions as we do today, but compared to the modern scholars, they had much more information available from the remaining khipukamayuq. However, the historical context and the political agenda of the colonial sources should also be taken into account.

If colors are indeed the primary carriers of meaning, the present-day classification of colors should be refined and approximated to the indigenous schemes. In other words, we should know if any two colors are perceived to be different and why. The present classification of colors needs to be abandoned in favor of a more native classification.

In my opinion, future research on the khipu should also center on establishing real patterns in the spinning/plying/color variation. For instance, Conklin writes that he finds the term variegated color misleading, because the actual pattern is more complex and standardized (Conklin 2002: 71-72). The systematic approach to the structure and color of the string would probably allow creating the first catalog of the khipu signs, what could be a decisive step on the way to decipherment.

 

Figure 6: color change within long knots (Urton in press: 106, Fig. 4.10)

Figure 6: color change within long knots
(Urton in press: 106, Fig. 4.10)

 

APPENDIX: TABLE 1

Categories of service in the Inka tribute record before the imposition of the Spanish tribute scheme (Urton 1998: 426, Table 1)

Form of service

Object(s) of the Activity

hacer

to make, do

paredes

walls

tinturas y colores

tints and dyes

sal

salt

coca

 

suelas

sandals

platos y escudillas

plates and bowls

ollas

bowls

ropa

clothing

 

sacar

to take

oro y plata

gold and silver

miel

honey

 

guardar

to guard

cuerpos

bodies (of deceased kings)

armas

arms, weapons

ovejas

sheep

chacaras

fields, crops

Indias

Indian women (kings women)

Chachapoyas/Quito

 

tambos

way stations

 

sembrar + comer

to plant/to eat

chacaras

fields, crops

aji

hot peppers

 

tomar

to take, to hunt

venados

deer

 

andar/ir

to walk/to go

con el Ynca

with the Inka

a Quito

to Quito

 

sacar

to take

 

 

guardar

to guard

 

 

sembrar + llevar

to plant/to deliver

 

 

hacer

to make, do

a Cuzco

to Cuzco

 

APPENDIX: TABLE 2

Categories of the Inka tribute according to several sources

Total Count

Khipu presented by the lords of Xauxa before the Royal Audiencia in 1561 (Murra 1990: Table 1)

Khipu from Canta, presented during the Visita real in 1549 (Murra 1982: 246-247)

The khipu presented at the inspection of Guancayo in 1571 (Murra 1982: 252-253)

Huanuco Labor Assignment provided during the inspection in 1562 (Julien 1982: 137, Table 5.6; see also the table above)

Pooled labor obligations of the Lupaca province (Julien 1982: 139-140, Table 5.8)

 

Item

Item

Item

People/Service

People/Service

1

barones

men

 

 

 

men at Inkas service

2

mujeres

women

 

 

 

women at Inkas service / women

3

ovejas de la tierra

llamas of both sexes

camelids

 

herders of Inca herds

 

4

carneros para su comida

male llamas

 

 

 

3b

ovejas, carneros, pacos, rancheados

stolen llamas

 

 

 

5

vestidos, llana, cumbi

clothes

woven cloth

cotton clothing, cumbi galanas, one blanket

weavers of qompi cloth

making cloth

6

making qompi cloth

7

 

 

making awasqa cloth

8

 

 

dye makers

 

9

frazadas

blankets

 

 

10

 

 

carpenters, transport to Cuzco

 

11

 

 

 

feather workers

12

 

 

 

making headbands

13

 

 

 

 

14

vestidos (rancheados)

stolen cloths

 

 

15

 

 

 

 

cultivators of land in Cuzco

cultivating land in Cuzco

15b

 

 

 

 

cultivators of other Inka lands

cultivating elsewhere

15b2

 

 

 

 

 

transporting from there to Cuzco

16
16b

 

 

coca leaves

coca leaves (baskets or boxes for the Inka)

cultivators of coca, transport to Cuzco and Huanuco

 

17
17b

 

 

hot peppers

hot peppers

cultivators of aji fields, transport to Cuzco

 

18

 

 

charqui

charqui

 

making charqui

19
19b

maíz

maize

maize

maize

guard for corn, transport to Cuzco

contributing coastal maize

20

quinua (hanegas)

 

 

 

 

contributing quinua

21

papas (hanegas)

potatoes

 

 

 

contributing potatoes

22

 

 

 

 

 

contributing chuño

22b

 

 

 

 

 

contributing chuño to Cuzco

23

 

 

 

 

 

contributing kañawa

24

 

 

 

 

 

contributing other foods

24b

 

 

 

 

 

contributing other foods to Cuzco

19b

maíz (rancheado)

stolen maize

 

 

 

 

20b

quinua (rancheadas)

stolen quinua

 

 

 

 

21b

papas (rancheadas)

stolen potatoes

 

 

 

 

25

alpargatas

 

 

 

 

 

26

ojotas de cabuya

cabuya fiber sandals

sandals of cabuya fiber

sandals

sole preparer (for shoes), transport to Cuzco

making sandals

25b

alpargatas (rancheadas)

 

 

 

 

 

25b

ojotas (rancheadas)

stolen sandals

 

 

 

 

27

sobrecargas grandes

 

 

 

 

 

28

aderezos de caballos

horse dressing?

 

 

 

 

29

cantaros, ollas, tinajas

jugs and bowls

 

 

potters, transport to Huanuco

 

30

 

 

 

 

 

making varnish

31

chamelicos, porongos, escudillas

 

 

 

 

 

29b

cantaros (rancheados)

stolen jugs

 

 

 

 

31b

porongos (rancheados)

 

 

 

 

 

32

Gallinas de Castilla

chicken

 

 

 

 

33

huevos

eggs

 

 

 

 

34

perdices

partridges

 

 

 

contributing partridges

35

 

 

 

 

 

contributing ducks

36

leña rajada (cargas)

wool

 

 

 

contributing wool from the community herds

37

leña menuda (cargas)

wool

 

 

 

38

carbón (cargas)

charcoal

 

 

 

 

39

hierba (cargas)

grass

 

 

 

 

40

paja (cargas)

straw

 

 

 

 

41

chicha (cantaros)

 

 

 

 

 

42

toda fruta (cestillos)

all fruits

 

 

 

 

43

sal blanca (libros)

white salt

 

 

salt miners

salt miners

44

pescado (cestillo de una libra)

fish

 

 

 

contributing fish

45

 

 

 

 

 

contributing fresh fish

45b

 

 

 

 

 

contributing fresh fish to Cuzco

46

 

 

 

dried crayfish for the Inka

 

contributing dried fish

47

 

 

 

 

 

contributing fungi

48

 

 

 

 

 

contributing cohucho

49

 

 

 

dried guabas

 

 

50

 

 

 

 

feather gatherers

 

51

 

 

 

 

honey gatherers

 

52

 

 

 

 

hunters to go on royal hunt

 

53

 

 

 

wooden rodejones for the royal lineages

 

 

54

 

 

 

 

 

making copper bars for the Inka house

55

 

 

 

 

 

making copper axes

55

 

 

 

 

 

making slings

56

 

 

 

 

 

making bolas for hunting

57

 

 

 

 

gold miners

gold miners

58

 

 

 

 

silver miners

silver miners

59

 

 

 

 

 

lead miners

60

 

 

 

 

 

silver miners

61

 

 

 

 

 

people to build houses, walls

61b

 

 

 

 

masons in Cuzco

people to build houses in Cuzco

62

 

 

Indians for war

 

garrison of the Chachapoyas

soldiers

62b

 

 

 

 

garrison of Quito

 

62b

 

 

 

 

guard for the tambo at Huanuco

 

62b

 

 

 

 

guard for the women of the Inka

 

63

 

 

 

 

 

chasqui post runners

62b

cargadores, a la salida

bearers to leave

Indians as bearers

 

soldiers and carriers

 

64

yanaconas a la salida

servants to leave

relatives as yana-conas

 

yanaconas of Wayna Qhapaq

yanaconas (men and women)

 

 

 

 

yanaconas for the weapons of Thupa Inka

 

64b

 

 

 

 

guards for the body of Wayna Qhapaq

 

65

 

 

 

 

 

children for sacrifice

65b

 

 

 

 

 

people for sacrifice

66

 

 

 

 

 

daughters of kurakas for concubines

67

 

 

 

 

 

women to serve the state cults

68

 

 

 

 

 

mitimas

69

ovejas a la salida

llamas to leave

 

 

 

livestock

70

corderos a la salida

lambs to leave

 

 

 

 

71

hanegas de maiz para el camino

maize for travel

 

 

 

 

72

quinua para el camino

quinua for travel

 

 

 

 

73

papas (hanegas) para el camino

potatoes for travel

 

 

 

 

 

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Quilter, Jeffrey
2002    Yncap Cimin Quipococs Knots
In: Narrative Threads: Accounting and Recounting in Andean Khipu, Jeffrey Quilter and Gary Urton, eds. P. 197-222
University of Texas Press, Austin

Salomon, Frank
2002    Patrimonial Khipu in Modern Peruvian Village: An Introduction to the Quipocamayos of Tupicocha, Huarochiri
In: Narrative Threads: Accounting and Recounting in Andean Khipu, Jeffrey Quilter and Gary Urton, eds. P. 293-319
University of Texas Press, Austin

Sarmiento de Gamboa, Pedro
1999    History of the Incas (trans. by Clements Markham)
Dover Publications, Inc., Mineola, NY

Urton, Gary
In press    Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records
University of Texas Press, Austin

2002a    An Overview of Spanish Colonial Commentary on Andean Knotted-String Records
In: Narrative Threads: Accounting and Recounting in Andean Khipu, Jeffrey Quilter and Gary Urton, eds. P. 3-25
University of Texas Press, Austin

2002b    Recording Signs in Narrative-Accounting Khipu
In: Narrative Threads: Accounting and Recounting in Andean Khipu, Jeffrey Quilter and Gary Urton, eds. P. 171-196
University of Texas Press, Austin

2001    A Calendrical and Demographic Tomb Text from Northern Peru
Latin American Antiquity 12 (2): 127-147
Society for American Archaeology

1998    From Knots to Narratives: Reconstructing the Art of Historical Record Keeping in the Andes from Spanish Transcriptions of the Inka Khipus
Ethnohistory 45 (3): 409-438
American Society for Ethnohistory

Garcilaso de la Vega
1966    Royal Commentaries of the Incas And General History of Peru, vol. 1, 2 (trans. by Harold V. Livermore)
University of Texas Press, Austin & London

Whittaker, Gordon
1993    The Study of North Mesoamerican Place-Signs Indiana 13: 9-38
Berlin

Zuidema, R. Tom
1982    Bureaucracy and Systemic Knowledge in Andean Civilization
In: The Inca and Aztec States, 1400-1800: Anthropology and History, George A. Collier, Renato I. Rosaldo, John D. Wirth, eds. P. 419-458
Academic Press, Inc., London

 


1 According Urtons estimations, there are about 600 khipu in public or private hands around the world, although the provenience of most khipu is unknown (Urton in press: 2).

2 They had another method of knowing and understanding what had been received from the contributions in the provinces, what provisions were stored on the routes that the king would take with his army or when he was visiting the provinces, how much was in each deposit, how much was delivered out. And this method exceeded in artifice the cadastres used by the Mexicans for their calculation (cited in Locke 1923: 34)

3 They recorded the number of men who went to the wars, how many died in them, and how many were born and died every year, month by month. In short they may be said to have recorded on their knots everything that could be counted, even mentioning battles and fights, all the embassies that had come to visit the Inca, and all the speeches and arguments the king had uttered. But the purpose of the embassies or the contents of the speeches, or any other descriptive matter could not be recorded on the knots, consisting as it did of continuous spoken or written prose, which cannot be expressed by means of knots, since these can give only numbers and not words. To supply this want they used signs that indicated historical events or facts or the existence of any embassy, speech, or discussion in time of peace or war. Such speeches were preserved by the quipucamayus by memory in a summarized form of a few words: they were committed to memory and taught by tradition to their successors and descendants from father to son

Similarly the harauicus, who were their poets, wrote short, compressed poems, embracing a history, or an embassy, or the king's reply. In short, everything that could not be recorded on the knots was included in these poems, which were sung at their triumphs and on the occasion of their greater festivals, and recited to the young Incas when they were armed knights. Thus they remembered their history (Garcilaso de la Vega 1966: 331-332)

4 The knots were arranged in order of units, ten, hundreds, thousands, tens of thousands, and seldom if ever passed a hundred thousand The greatest number, say tens of thousands, was knotted at the upper end of the threads, the thousands lower down, and so on down to units (Garcilaso de la Vega 1966: 330).

5 The Indians made threads of various colors, some were of a single hue, others of two, others of three or more, for single or mixed colors all had separate significances. The threads were closely twisted with three or four strands, as thick as an iron spindle and about three quarters of a vara in lengthThe colors showed what subject the thread was about, such as yellow for gold, white for silver, and red for warriors (Garcilaso de la Vega 1966: 329-330).

6 Some of these strings had finer threads of the same color attached, serving as offshoots or exceptions from the general rules (Garcilaso de la Vega 1966: 330).

7 These were knots in different threads of various colors, which were placed in order, though not always in the same order (emphasize is mine A. T.): sometimes one color came before another, and on other occasions they were reversed. This type of communication was a system of ciphers by which the Inca and his governors agreed on what was to be done, and the knots and colors of the threads implied the number of men, arms, or clothes or supplies or whatever it was that had to be made or sent or prepared (Garcilaso de la Vega 1966: 329)

In the same way records were kept of their laws, ordinances, rites, and ceremonies. From the color of the thread and the number of the knots, they would tell what law prohibited any particular offence and what penalty was to be applied to anyone who broke it. They could say what sacrifice or ceremony was performed in honor of the Sun on such-and-such a festival. They could state what ordinance or privilege afforded protection to widows, or the poor, or wayfarers. In this way they could provide information on any other matters that had been memorized and handed down by tradition (Garcilaso de la Vega 1966: 333)

8 For instance, the repeating pattern of colors suggests that they may have functioned as a positional system device