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Signs of the Inka Khipu

[ Archaeology ]

Signs of the Inka Khipu

Binary Coding in the Andean Knotted-String Records

By Gary Urton

In this book, Gary Urton sets forth a pathbreaking theory that the manipulation of fibers in the construction of khipu created physical features that constitute binary-coded sequences which store units of information in a system of binary recordkeeping that was used throughout the Inka empire

2003

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6 x 9 | 216 pp. | 21 illustrations, 24 figures, 5 tables

ISBN: 978-0-292-78540-3

In an age when computers process immense amounts of information by the manipulation of sequences of 1s and 0s, it remains a frustrating mystery how prehistoric Inka recordkeepers encoded a tremendous variety and quantity of data using only knotted and dyed strings. Yet the comparison between computers and khipu may hold an important clue to deciphering the Inka records. In this book, Gary Urton sets forth a pathbreaking theory that the manipulation of fibers in the construction of khipu created physical features that constitute binary-coded sequences which store units of information in a system of binary recordkeeping that was used throughout the Inka empire.

Urton begins his theory with the making of khipu, showing how at each step of the process binary, either/or choices were made. He then investigates the symbolic components of the binary coding system, the amount of information that could have been encoded, procedures that may have been used for reading the khipu, the nature of the khipu signs, and, finally, the nature of the khipu recording system itself—emphasizing relations of markedness and semantic coupling. This research constitutes a major step forward in building a unified theory of the khipu system of information storage and communication based on the sum total of construction features making up these extraordinary objects.

  • Preface and Acknowledgments
  • Chapter 1. Memory, Writing, and Record Keeping in the Inka Empire
  • Chapter 2. Theory and Methods in the Study of Khipu Binary Coding
  • Chapter 3. The Physical Components of Khipu Binary Coding
  • Chapter 4. The Linguistic Components of Khipu Binary Coding
  • Chapter 5. Khipu Sign Capacity and Code Conversion
  • Chapter 6. Sign Theory, Markedness, and Parallelism in the Khipu Information System
  • Chapter 7. Conclusions
  • Appendix. Tabular Description of Khipu UR19 from Chachapoyas
  • Notes
  • Bibliography
  • Index

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It is one of the great ironies of the age in which we live that the cacophony of computer-based, electronically produced information that suffuses our every waking moment is carried into our consciousness on patterned waves of just two signs: 1 and 0. This, of course, is no news. We have all been made aware since the dawn of the present Information Age that the ongoing revolution in computing technology rests on a system of binary coding. I discuss the matter at length below, but I would clarify here that by "binary coding," I mean a system of communication based on units of information that take the form of strings of signs or signals, each individual unit of which represents one or the other of a pair of alternative (usually opposite) identities or states; for example, the signal may be on or off (as in a light switch), positive or negative (as in an electrical current), or 1 or 0 (as in computer coding). One can argue that it is the simplicity of binary coding that gives computing technology and its information systems their great flexibility and seemingly inexhaustible expansiveness. In this study, I explore an earlier and potentially equally powerful system of coding information that was at home in pre-Columbian South America and which, like the coding systems used in present-day computer language, was structured primarily as a binary code.

After the above grandiose introduction, it may come as a letdown to the reader to learn that we do not yet know, in fact, how to interpret or read the majority of the information that is presumably encoded in the recording system that I describe and analyze in this book. The system in question is that of the Inka khipu. Khipu (knot; to knot) is a term drawn from Quechua, the lingua franca and language of administration of the Inka Empire (ca. 1450-1532 C.E.). The khipu were knotted-string devices (see Figure 1.1) that were used for recording both statistical and narrative information, most notably by the Inka but also by other peoples of the central Andes from pre-Inkaic times (see Conklin 1982; Shady, Narváez, and López 2000), through the colonial and republican eras (Brokaw 1999; Murra 1975; Platt 2002; Urton 1998, 2001), and even-in a considerably transformed and attenuated formdown to the present day (Mackey 1970, 2002; Núñez del Prado 1990; Ruiz Estrada 1998; Salomon 2002).

I estimate from my own studies and from the published works of other scholars that there are about 600 extant khipu in public and private collections around the world (see Chapter 2). Although provenience data are notoriously sketchy for museum samples of khipu, what information we do have tends to support the conclusion that most samples were looted from grave sites along the central and south coast of Peru during the late nineteenth and early twentieth centuries. A recent discovery of thirty-two khipu in burial chambers in the northern Peruvian Andes is consistent with the presumed funerary disposal of these devices (see Urton 2001 for a discussion of the possible significance of this context for khipu disposal).

Europeans became aware of the knotted-string devices used by the indigenous Inka record keepers from the earliest days following the Spanish Conquest, which began in 1532. Hernando Pizarro, the brother of the leader of the conquistadors and (later) marquis, Francisco Pizarro, described an encounter that he and his men had with khipu keepers on the royal road from the highlands down to the central coast of Peru in 1533. Pizarro notes that when he and his men removed some goods from one of the Inka storehouses, the record keepers "untied some of the knots which they had in the deposits section [of the khipu], and they [re-]tied them in another section [of the khipu]" (H. Pizarro 1920 [1533]: 175 and 178).

Following this initial reference to khipu, accounts of these devices appear with considerable frequency in the Spanish chronicles and documents recorded throughout the first few decades of the establishment of the colony (see Urton n.d.a). Khipu were one of the principal sources of information used by the Spaniards as they began to compile records pertaining to the former inhabitants of the empire. The former Inka record keepers--known as khipukamayuq (knot maker/keeper)--supplied colonial administrators with a tremendous variety and quantity of information pertaining to censuses, tribute, ritual and calendrical organization, genealogies, and other such matters from Inka times. While numerous colonial writers in Peru left accounts of the khipu that inform us on certain features and operations of these devices, none of these accounts is extensive or detailed enough to put us on solid ground in our attempts today to understand exactly how the Inka made and consulted (that is, read) these knotted and dyed records.

An issue of utmost interest and concern to several scholars who are intensively studying these devices today (see esp. Quilter and Urton 2002) centers around the question of whether the khipu recording system should be characterized as a system of "mnemonics," or if it may in fact have constituted a system of "writing." In a word, the matter under dispute is whether khipu were (respectively) string-and-knot-based configurations whose purpose was to provide "cues" to aid the Inka administrator who made any particular sample to recall a specific body of memorized information, or if these devices were constructed with conventionalized units of information that could be read by khipu makers throughout the empire. I should state that I am primarily an adherent of the latter of these two starkly differentiated and ultimately caricatured views of khipu records (see Urton 1998, 2002). In fact, I suspect that the final solution we will arrive at regarding the types of information retained on these devices will look more like a combination of the two forms of record keeping alluded to above.

In this introductory chapter, I first provide an overview of these two differing points of view on the question of what kind of recording system the khipu may have represented as they have emerged in publications since the beginning of the twentieth century. I then lay out in a general way the new approach to analyzing and interpreting the khipu developed in this book. Before beginning, it may be helpful to the non-Andeanist reader for me to describe the basic features of these remarkable devices, the khipu.

Khipu Structures

In general terms, khipu are composed of a main, or primary, cord to which are attached a variable number of what are termed pendant strings (see Figure 1.2). Many samples have only a few pendant strings, while a couple have upward of 1,500 pendants. To state definitively the average number of pendant strings on all khipu would be a difficult under taking, particularly as our studies of some collections are incomplete. As an example, however, I note that for a collection of thirty-two khipu recently discovered in Chachapoyas, in northern Peru (see Urton 2001 and below), the average number of pendant strings on the twenty-two samples that were well enough preserved to allow for close study was 149 (the range is between 6 and 762).

Primary cords usually have a diameter in the range of 1/2 to 2/3 cm, and they often display complex bi- or multicolored spin and ply patterns. It is not uncommon for primary cords to be finished off with a "wrapping" composed of a cord made of two or three pairs of differently colored spun and plied yarns. In some cases, tassels may be tied onto primary cords indicating divisions or classifications (of some manner) of the information registered on groups of pendant strings. I have examined some twenty khipu samples in various collections that have large needlework "bundles" that terminate one end of the primary cord. Salomon has described similar bundles on a few samples of khipu used today for ritual purposes in the Peruvian central highland community of Tupicocha (Salomon 2002; see below). Such "end ornaments" in Tupicocha are generally referred to as pachacamanta ("about/concerning the hundred"; Salomon 2002: 303). Given that the unit of one hundred tribute payers was an important organizational unit in Inka administration--often used as a synonym for the sociopolitical and communal labor groupings referred to as ayllu--these khipu ornaments as retained in the samples from Tupicocha today may offer a clue to the significance of such ornaments on archaeological khipu. That is, they may have indicated the administrative class of khipu in question, as well as its general subject matter and the magnitude of units recorded.

Pendant strings may have attached to them secondary, or subsidiary, strings, which may, in turn, carry subsidiary (i.e., tertiary) strings, and so on. Some khipu also display top strings; these strings are attached in such a way that they leave the primary cord in the opposite direction from the pendant strings. In some cases, the attachment of a top string is by means of a loop that binds the top string into the attachments of a group of pendant strings across the primary cord (see Figure 1.5).

As I discuss in greater detail below, on most khipu, knots of three different types were tied into pendant, subsidiary, and top strings. In the case of those khipu that recorded quantitative values (rather than narrative records; see below), the three types of knots are tied in patterned arrangements of clusters along the body of strings to indicate increasingly higher powers of ten (see Figure 1.6; for further overviews of khipu structures and construction techniques, see Arellano 1999; Ascher and Ascher 1969, 1975, 1997 [1981]; Conklin 2002; Loza 1998; Mackey 2002; Mackey et al. 1990; Pereyra 1997, 2001; Radicati di Primeglio 1979; Salomon 2002; and Urton 1994, 2001, 2002).

Some of the features of khipu, such as the decimal arrangement of knots on many samples, are described for us in Spanish accounts written during the colonial era either by Spaniards or by literate Andeans (especially Garcilaso de la Vega and Felipe Guaman Poma de Ayala). For an appreciation of certain characteristics of khipu construction, however, we have had to wait for the results of careful scientific study of museum samples in modern times. With this understanding of some of the main features of the khipu, we can now turn to the question of the possible nature of the signs encoded on these devices; that is, was this a memory-cueing device? Was it a system of writing? Or was it some other type of record keeping?

Mnemonic Schemes and Devices

I should begin by establishing the parameters to be taken into account in the discussion below of memory and mnemonic devices (for excellent treatments of the nature of memory in Andean societies, past and present, see Kaulicke 2000: 5-10; and Howard 2002). I note, on the one hand, that I set aside from consideration the large body of works relating to the topic of mnemonics undertaken from the psychobiological paradigmatic perspective. Although such studies offer many insights into the capacities and motivations of individual processes of remembering and recalling, my concern here is not with experimental instances of what, when, or how individuals remember, recollect, or otherwise behave with respect to a piece of memorized information. In this regard, I am in agreement with Maurice Halbwachs when he wrote:

One is rather astonished when reading psychological treatises that deal with memory to find that people are considered there as isolated beings. These make it appear that to understand our mental operations, we need to stick to individuals and first of all, to divide all the bonds which attach individuals to the society of their fellows. Yet it is in society that people normally acquire their memories. It is also in society that they recall, recognize, and localize their memories. (1992 [1941/1952]: 38)

My concern rather is with placing memory, recollection, and recitation in social contexts, as well as with understanding how (i.e., in what manner and with what sociopolitical motives and consequences) people commit information to memory schema, transmit that information to other people, and then interact with others through or in relation to that body of memory-based information. For memory routines, regimes, and forms of interaction of these types, the sociocultural, interactional, and intellectual paradigms directing anthropological theory and practice are, in my view, preferable to those of psychology.

However, I should also state that I am not concerned here with the kinds of issues--at the other end of the spectrum of inclusiveness of human interactions--addressed in Paul Connerton's now classic study How Societies Remember (1989). That is, it is not my intent to analyze the kinds of large-scale collective rituals and ceremonies through which community, state, or national values, histories, and identities were formulated, reproduced, and commemorated publicly. Rather, I am concerned with what we may now define as the middle range of the work of memory and notation, that between the individual and the collectivity. This entails both individuals and classes of people (e.g., administrators, historians) within communities who produced and maintained records on such matters as population censuses, tribute (whether paid, projected, or levied), genealogical relations among the living and connections between the living and the dead, mythohistories, and so on. In most ancient and modern states, such records have been retained in written documents. The big question we will address here is: Were the khipu the "written documents" of the Inka Empire? In addressing this question, we must begin by sorting out the difference and the relationship between mnemonics and writing.

My Merriam Webster's dictionary (1978 [1904]) defines mnemonics as: "1. the science or art of improving the memory, as by the use of certain formulas. 2. formulas or other aids to help in remembering." Thus, for instance, the formula that begins "thirty days hath September, April, June, and November" is a mnemonic device that helps me to remember the number of days in the months of the year. Although this formula is generally spoken aloud or under the breath, it can obviously (as above) be written.

Regarding the possible role of formulas in khipu record keeping in Inka times, I strongly suspect that there were configurations of strings, knots, colors, and other features that were linked to, and therefore provided cues for, recitations of formulaic information on the order of the "thirty days" formula described above. By analogy with other settings in which formulas were central elements in very complicated traditions of reciting sagas, epics, and other long memorized narratives (e.g., see Ong 1995 [1982]: 58-60 on the use of formulas in ancient Greek and 1960s-1970s Yugoslavian oral narration), it is reasonable to suppose that formulas may have formed important components of the narrative strategies linked to khipu recitations. Some of these may be at least partially recoverable from close study of colonial chronicles and documents (e.g., Julien 2000), from the few surviving instances of ritualism connected with the display of khipu today (Salomon 2002), as well as from the study of semantic strategies and syntactic structures of Quechua discourse and poetics (e.g., Howard 2002; Howard-Malverde 1990; Mannheim 1998).

Another common type of mnemonic device is the deceptively simple string tied around the finger to help recall some piece of memorized information. In the string-around-the-finger type of memory aid, one first determines the information (e.g., the message or task) one wishes to recall by means of the memory aid. The information is then linked by the mnemonist to a memory-cueing device, which in this case is the piece of string tied around the finger. The person then goes about his/her business, but upon seeing or becoming aware of the extraordinary presence of a string tied around his/her finger--surprise being the trigger for cueing in this particular system--the mnemonist remembers or recites the message, or performs the task, which he/she had arbitrarily connected to the string in tying it around his/her finger.

To explore somewhat further the nature and implications of the string-around-the-finger cueing device, I believe it is fair to say that we generally have the understanding that no one other than the wearer of such a device will know its meaning, unless the wearer indicates the meaning to another person. For instance, if you were to see a string tied around my finger, you might suspect that I was trying to remember something by means of that string; however, you could not know what the content of that message to myself was unless I told it to you. This is because such devices are memory aids; they are generally not composed of signs having conventional values. It is particularly relevant to the issues we are concerned with in this study to note that if I were to forget the information I had originally attached to a string tied around my finger, not even I, its creator, could retrieve the message from looking at the string; this is because there is, as I have said, no information encoded in or on the string.

Another mnemotechnic device bearing a similar information content to the string-around-the-finger type is the rosary. This latter device, composed of beads or other counters strung together on a string, is used as a prompting device; the user runs his or her forgers along the beads while reciting a fixed, memorized formula, or credo. Although the rosary differs from the string around the finger in that the former is linked to complex, shared formulae, whereas the latter is a sort of one-off prompt for a private message, nonetheless, the two devices are similar in one important respect: the message that is prompted by their use is not recorded in (or on) the memory-cueing device itself. That is, the beads are not signs; they are merely place holders. Thus, if the user of either of these memory aids forgets the message that was originally intended to be prompted by the device, the message cannot be recovered from information (i.e., signs with conventionalized meanings) on the object itself. This is because neither of these contrivances is, in fact, a device for record keeping; rather, they are prompts for information stored in the memory of the user(s).

Some colonial commentators (e.g., Molina ["el Cuzqueño"] 1916 [1573]: 23-24), as well as one of the most notable early modern students of the khipu (Locke 1923: 31), suppose that these devices were string-around-the-finger or rosary-type memory aids. If this was the case, then we cannot be sanguine about our prospects for ever reading, or giving an authoritative interpretation of, one of these devices, as all of the native khipu mnemonics specialists of these objects have long since died. However, I believe, and will attempt to demonstrate here, that such a comparison is profoundly inappropriate for several reasons, most notably because the khipu exhibits far greater complexity and patterning in its structure and organization than the rosary or other similar devices (e.g., incised "message sticks," etc.). I return to this comparison in the conclusions, by which time I believe the reader will agree that the comparison between khipu and rosaries and other similar devices is deeply misleading and irrelevant.

A more complicated mnemonic device, but still of the general class we have just been considering, is that of the Medieval "memory theater." This was a mnemonic method whereby a usually large and detailed body of information was keyed to--that is, placed mentally inside of a complex, often architectural, structure, like a building with multiple rooms with pictures on the walls, for example. When the mnemonist wanted to recall the information, he/she would do so by making a tour of the mental space constructed, retrieving pieces of the narrative that had been placed at certain loci within the structure (see Spence 1984; see also Hasenohr 1982 for a fascinating account of the use of the segments of the hands as a structure for memorizing and recalling information). The principal source on the memory theater is Frances Yates's masterful study The Art of Memory (1966; see also Carruthers 1993). Yates details the varied principles behind this combined memory structure and routine, beginning with its earliest forms in the classical Mediterranean world and proceeding to the Renaissance. In the interest of brevity, I provide below an excellent summary of European memory theaters as recounted in Patrick Hutton's History as an Art of Memory:

The art of memory as it was traditionally conceived was based upon associations between a structure of images easily remembered and a body of knowledge in need of organization. The mnemonist's task was to attach the facts that he wished to recall to images that were so visually striking or emotionally evocative that they could be recalled at will. He then classified these images in an architectural design of places with which he was readily familiar. The landscape of memory so constructed was an imaginary tableau in which a world of knowledge might be contained for ready reference. It was in effect a borrowed paradigm, the logic of whose imaginary structure gave shape to the otherwise formless knowledge he wished to retain. (1993: 27)

We must ask whether or not the memory theater, with its association between a large, complicated body of information organized and attached to places within a complex structural (e.g., architectural) mental image, is an appropriate model to adopt for the kind of "recording" system represented by the khipu. In my reading of certain views of the khipu recording system (see below), it seems that some commentators would answer this question in the affirmative. If this was the case, we would again (i.e., as with the string-around-the-finger or rosary mnemonic devices) be unlikely to be able to retrieve much, if any, information from study of these devices today.

I must say here, however, that I am skeptical about the possibility that the memory theater offers a reasonable model for the intellectual tradition and mnemonic procedures of a recording system in which the structures to which memories would have been projected were actual physical, constructed objects-like the khipu. It is one thing (certainly in social terms) to key memories to a mental image and quite another to key them to a complex, portable fabrication that can be (and was, as we read in the chronicles) carried around, studied and restudied, changed in various ways, and stored away for later referral. We must also ask, if the khipu was an empty physical schema onto which memories were projected, why would the khipukamayuq have needed or wanted to construct such objects in the first place? Such a practice seems uncalled for and unreasonable because, first, the record keepers could have accomplished the same ends with a purely mental image, as was done in the European memory theater, since a mental image is even more portable than a khipu! And second, since (according to this interpretation) the khipu would not have contained any actual information in the form of signs with conventionalized values, what use would it have served? The khipukamayuq could not have recovered lost or forgotten information from it, so why make it in the first place?

I should note in regard to these matters that the chronicler Sarmiento de Gamboa, who interviewed and compared the historical accounts of over one hundred khipukamayuq (see Urton 1990: 18-19), made a clear distinction between the work of memorizing historical accounts and recording information on the khipu. That is, Sarmiento first notes that

... to supply the want of letters, these barbarians had a curious invention which was very good and accurate. This was that from one to the other, from fathers to sons, they handed down past events, repeating the story of them many times, just as lessons are repeated from a professor's chair, making the hearers say these historical lessons over and over again until they were fixed in the memory. (Sarmiento de Gamboa 1999 [1572]: 41)

It will be noted that Sarmiento does not suggest that the memorized information is being keyed to khipu by these memory artists. This accords with what we learn from students of oral recitations, who stress that it is versification and repetition, not the reliance on a mnemonic device, that are the keys to memorizing long passages (see Lord 1960; Notopoulos 1938: 469; Ong 1995: 60). To return to Sarmiento's testimony, several lines after the above passage he goes on to say:

Finally, they recorded, and they still record, the most notable things which consist in their numbers (or statistics), on certain cords called quipu, which is the same as to say reasoner or accountant. On these cords they make certain knots by which, and by differences of colour, they distinguish and record each thing as by letters. It is a thing to be admired to see what details may be recorded on these cords, for which there are masters like our writing masters. (1999: 41)

Thus, Sarmiento distinguishes between the work of memorizing long historical narratives, which did not involve the khipu, and that of recording statistical data, apparently with notations giving some manner of contextual information, by means of the khipu. We will see in other sources, however, that the information recorded on the khipu was of a somewhat more complicated nature, more so than is suggested by Sarmiento in the above quotation.

The last example of a form of mnemonics that I review here will, in fact, move us across the border that usually separates mnemonics and writing. I am referring to the sort of memory aid we commonly make for ourselves, such as a notation I might write on my desk calendar: "lunch, John." Were I to see such a notation to myself on my calendar for tomorrow's date, I would know immediately that this pair of words, written in alphabetic script, was a mnemonic for the complete message: "At noon tomorrow, I am scheduled to have lunch with my colleague John Smith." Now, mnemonic messages of almost precisely this level of abstractness (i.e., "lunch, John") make up the majority of the earliest texts written in the cuneiform script, beginning around 3200 B.C.E. As we will see, specialists in cuneiform tend to be quite hesitant about classifying such notations as "writing." This is because, in the earliest cuneiform texts, the sign units making up such mnemonic notations are composed of logograms--that is, nonphonetic word signs--which are generally not classified as "true writing."

In their incisive and highly informative study Archaic Bookkeeping (1993), Hans Nissen, Peter Damerow, and Robert Englund lay out in some detail the processes and general line of development through which writing emerged in the ancient Near East. To begin with, and as has been forcefully and persuasively argued by Denise Schmandt-Besserat (1996), the development of true writing in Mesopotamia followed a long period during which notations were made in the form of clay tokens of various types. These token-based accounting and recordkeeping traditions began around 9000 B.C.E. and evolved into the first inscribed texts, which appeared around 3200 B.C.E. (Schmandt-Besserat 1996: 117-122). As Nissen, Damerow, and Englund make clear, the earliest written texts generally contain numerical notations as well as a relatively limited number of ideographic signs (i.e., nonphonological logograms):

Unfortunately, on most of the archaic tablets, in particular on those from script phase Uruk IV [ca. 3100 B.C.E.], the information given is kept as concise as possible. Everything expected to be known by the reader was omitted by the scribe. Thus there was obviously no need to elaborate on syntactic relationships, for example, to include extra information about the sender or the receiver of goods involved. It apparently sufficed to report the quantities of the goods in question. The nature of these products was often obvious from the type of numerical signs employed ... At the end of the text, the name of the responsible person or institution was added ... We are thus merely able to detect a relationship between the entries, but not the nature of this relationship. (1993: 20-21; my emphasis)

One such text, dating to script phase Uruk III (ca. 3000 B.C.E.), is shown in Figure 1.7. This text establishes, in some syntactically unspecified manner, a relationship between two cattle and the temple of the goddess Inanna (Nissen, Damerow, and Englund 1993: 21, Fig. 23).

It will be seen that, in terms of the lack of syntactic information in the two notations, the mnemonic text shown in Figure 1.7 is not significantly different from the mnemonic text "lunch, John" that I described earlier as one I might write on my own calendar. However, in terms of the nature of the signs employed in the two inscriptions, there is a profound difference, for the text shown in Figure 1.7 is composed of (nonphonetic) logographic sign units, whereas the signs that I write on my calendar are phonologically based (i.e., alphabetic) sign units. Yet, I repeat, both inscriptions are "mnemonic aids."

We turn now to consider the interpretations of khipu as mnemonic devices. When we encounter (as we shall) references to these knottedstring constructions as "mnemonic devices," we should now insist on asking, What kind of mnemonic devices were they? Were they like strings tied around the khipukamayuq's finger? Were the knots empty of significance, like the counters of a rosary? Were khipu similar to structural (e.g., architectural) memory-theater-like configurations used in some manner for the recitation of carefully stored bodies of information? Were they like schematic logographic inscriptions? Or, perhaps most unlikely of all, could they have been syllabic, alphabetic, or other phonologically based notations? Just what kinds of mnemonic devices have scholars considered the khipu to have represented? Unfortunately, we will find that most theorists who have argued that the khipu represented mnemonic devices have been, to say the least, quite vague and unspecific in their definitions of this concept.

Before turning to look at the few explicit arguments characterizing the khipu as a mnemonic recording device, I want to state clearly that although I do not accept the basic tenets of the mnemonic interpretation of the khipu, at least not if it is limited to the memory-theater, string-around-the-finger, or rosary types of mnemonics, I think that memory undoubtedly played an important role in the reading of these devices. As William J. Conklin (2002), among others, has pointed out, all script systems represent mnemonic recording devices to one degree or another. Certainly this was true, as we have seen, of the earliest cuneiform economic texts, in which the clay tablets generally recorded only the numbers and nouns of economic transactions; however, in the hands of a knowledgeable Sumerian official, these skeletal texts could be embellished with modifiers and grammatical syntactical elements in the production of a narrative rendering of the transaction in question (see Nissen, Damerow, and Englund 1993: 116-117; and Sampson 1985: 50; on the related issue of the linkage between the logic of writing and the logic of divination in early Mesopotamia, see Manetti 1993: 2-5).

We find a similar situation to that described above in the case of the early texts produced in Linear B. As John Chadwick has noted: ". . . what mattered most to the users of these documents was the numerals. The numbers and quantities are the important details which cannot be confided to the memory; the remainder of the text is simply a brief note of what the numerals refer to, headings to enable the reader to identify the person or place associated with the quantity recorded" (1994 [1976]: 27; my emphasis). By reference to the tradition of recording "brief notes" identifying the objects modified by the numerals, we find ourselves again confronting the kind of mnemonics tradition-as in early cuneiform-that connects mnemonics and writing (in the case of Linear B, with syllabic and, to a lesser degree, logographic signs). This prompts us to ask whether or not those who argue that the khipu represented a "mnemonic" recording system would be willing to concede that certain of the string/knot/color combinations could have been accorded logographic values. If not, why not? But if so, then we are thereby at the doorstep of writing by means of the khipu.

Regarding the importance of memory in mnemotechnic and writing systems, I would also note that even in our own alphabetic script, the squiggles that we draw on a piece of paper-the letters of our alphabet-serve to remind us of arrangements of signs denoting groupings of sounds that go together to form the words we wish to indicate (or that have been indicated) in a written text.

On this matter, I would point out that a part of the testimony provided by one of our most interesting and seemingly knowledgeable sources on the khipu, the Peruvian Jesuit mestizo and supposed author of a lost chronicle Blas Valera, seems to confirm that the "reading" of a khipu may, in fact, have been the work of memory alone:

The tenacity of their memories is noticeably superior to that of Spaniards, even those of outstandingly good memory. 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 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. All this springs from the Indians' ingenuity and good memory." (cited in Garcilaso de la Vega 1966: 331)

Before we let the above portion of the testimony of Blas Valera carry the day with regard to the question of whether the khipu was a mnemonic device--at least one of the string-around-the-finger or the memory-theater type--or a writing system, we should note two further points that considerably complicate this picture. First, there is equally explicit testimony from other knowledgeable writers of the colonial period which states that the Inka did, in fact, "write" historical annals and other such discursive types of documents by means of the khipu (see Quilter and Urton 2002), and second, the above comments by Blas Valera are introduced by the following harangue against the Spaniards:

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. (cited in Garcilaso de la Vega 1966: 331)

Thus, Valera was arguing that even in his own time, the colonizers had remained essentially ignorant of how khipu functioned in record keeping. I think that before the matter is decided with respect to the connection between memory and writing in the khipu on the basis of a part of Blas Valera's testimony, we need to explore more fully--as I intend to do in the present study--what Valera referred to as the "theory and rules of their knots and accounts" (for a study of Blas Valera's ideas about and commentary on khipu, see Hyland 2002).

The Mnemonics Argument in Khipu Studies

A number of scholars who studied the khipu in the past, most notably L. Leland Locke (1912, 1923, 1928), as well as today (e.g., Rappaport and Cummins 1994, 1998), have argued that khipu constituted "mnemonic devices" whose purpose was to aid the khipukamayuq. in the recitation of information stored in the memory. We may imagine that we are viewing such a reading in one of the drawings by the latesixteenth-, early-seventeenth-century native chronicler Felipe Guaman Poma de Ayala (1980 [1615]; see Figure 1.8). The illustration depicts a khipukamayuq, on the right, reporting to the emperor, Topa Ynga Yupanqui, the contents of his khipu (whose information can be seen knotted into the strings of this device), which presumably contains an accounting of the materials in the state warehouses (collcas) shown in the drawing.

Most proponents of the mnemonics interpretation of khipu records have maintained not only that the khipu served as an arrangement of visual and tactile "cues" for the recall of the information retained in the memory of its maker, but also that there were no conventional signs or widely shared translation values assigned to khipu structures that would have allowed one khipukamayuq to read another's khipu or that could have served as a basis for a confirmation of readings among various record keepers throughout the empire. The view characterizing the khipu as based on nonshared, idiosyncratic recording values, or procedures, draws its primary support from the testimony of the mid-seventeenth-century Jesuit chronicler Bernabé Cobo. As Cobo noted:

In place of writing they used some strands of cord or thin wool strings, like the ones we use to string rosaries; and these strings were called quipos. By these recording devices and registers they conserved the memory of their acts, and the Inca's overseers and accountants used them to remember what had been received and consumed. A bunch of these quipos served them as a ledger or notebook.... There were people designated for this job of accounting. These officials were called quipo camayos and the Incas had great confidence in them. These officials learned with great care this way of making records and preserving historical facts. However, not all of the Indians were capable of understanding the quipos; only those dedicated to this job could do it; and those who did not study quipos failed to understand them. Even among the quipo camayos themselves, one was unable to understand the registers and recording devices of others. Each one understood the quipos that he made and what the others told him. (Cobo 1983 [1653]: 253-254; my emphasis)

Since Cobo's testimony is so powerful and seemingly authoritative, especially on the question of the nonstandardized, nonconventional, and nonreciprocally readable nature of the khipu, it is important to mention a couple of conditions regarding his testimony and the times in which he lived that bear on the question of what Cobo may and may not have been aware of. In the first place, Cobo's account was published in 1653, 130 years after the beginning of the Iberian invasion of western South America. Thus, a lot of time had passed since khipu were used openly for official record keeping in day-to-day settings in communities throughout the Andes, much less in Cusco, where Cobo spent most of his time and collected most of his data (Cobo 1983: 100-101). Cusco was the former capital of the Inka Empire and was, by Cobo's time, a heavily Hispanicized city (see MacCormack 2001). However, and more to the point of our concerns here, the khipu had actually been banned, condemned as idolatrous objects, and ordered burned some 70 years before Cobo penned his chronicle! This disposition had occurred as an act of the Third Council of Lima, in 1583 (Urton 1998; Vargas Ugarte 1959). Thus, Cobo himself probably never witnessed khipu being handled, much less read, in circumstances that were not fraught with considerable tension or negative, censorious attitudes on the part of Spaniards.

The second point to make with regard to Cobo's testimony is that among those earlier chroniclers--some of whom Cobo used as his sources--who wrote about khipu before the Third Council, during a period when these devices were more commonly seen, used, and produced as sources of historical and legal testimony (e.g., Cieza de León, Sarmiento de Gamboa, Garcilaso de la Vega), none states that khipu could only be read by the person who made them (see Urton n.d.a). For these reasons, I think it is important that we not allow the testimony of this one late chronicler (i.e., Cobo) to be the sole voice establishing for us the parameters of the readability and potentially shared, conventionalized nature of these records.

The situation discussed above regarding the readability of the khipu concerns those records that formed a part of the official documentation of the Inka state, as opposed to any knotted-string records that might have been produced for individual use. This latter point is important, because what is at issue here is not whether or not people were capable of producing private, idiosyncratic record-keeping devices (which they obviously were), but rather, whether or not state records that were kept by local, regional, and imperial administrators would or would not have been subject to some requirements of conventionality, transparency, and comparability of recording and reading.

The earliest sustained argument in the modern era for the status of the khipu as a mnemonic device appeared in the work of L. Leland Locke (esp. 1923). Locke compared the khipu to such undoubted mnemonic devices as rosaries and message sticks. From his studies of some forty-two khipu in the American Museum of Natural History, Locke concluded that the khipu was used primarily to sign numbers and that it did not represent a conventional scheme of writing (1923: 31-32; see below). In the course of this study, I show that Locke, in fact, failed to take into account even one-half of the total information encoded in the khipu, and that, therefore, his conclusion to the effect that the "evidence" does not warrant classifying the khipu as a writing system is highly questionable. I address Locke's conclusions on the nature of the khipu record-keeping system in Chapter 7.

The most highly developed form of the mnemonic argument in recent times is in a series of important articles dealing with literacy in the early colonial Andes published by Joanne Rappaport and Tom Cummins (e.g., 1994, 1998). One consistent theme of these scholars' work has been that the introduction of alphabetic literacy into the Andes at the time of the conquest represented a force for significant intellectual, technological, political, and ideological transformation for the native Americans. One reason for this, according to Rappaport and Cummins, was that Andean peoples did not have prior experience with a system of writing--specifically, not with a graphic, alphabetic script (on this subject, see also Quispe-Agnoli 2000). The researchers' primary interest in this series of studies is in exploring the consequences of the Andean confrontation with and consumption of an alphabetic script system and the political--but not economic or numerical (see below)--system that it supported.

In undertaking this critique, I want to stress that I believe that Rappaport and Cummins are completely correct in their analyses of the nature and significance of the transformations wrought by the imposition of alphabetic literacy in the early colonial Andean world. The questions I raise below regarding their work concern what is a relatively minor point for their own arguments and research agenda but one that is of much greater significance for the problems I am concerned with here.

Among Rappaport and Cummins's statements about the nature of khipu mnemonic records, we read the following:

The Andean object which could be said to correspond most closely to the document is the quipu, a mnemonic device of coloured and knotted strings used in Andean cultures to recall various categories of information.... The act of writing to communicate presupposes literacy, while mnemonics is based instead on the memorization of facts which are represented in an object. The object itself cannot abstractly communicate knowledge as writing does. Rather, it stands for categories of knowledge which are then specified in relation to memorized data. Thus, the quipu and the quipucamayoc (the one who has memorized the quipu) are not independent of each other in the way that the writer and reader are. (1994: 100; my emphases)

It is clear that Rappaport and Cummins support Cobo's understanding that khipu were not based on shared traditions of signing and meaning, as they state unequivocally that the khipukamayuq and his khipu were inseparable. Beyond that, however, we are confronted in this quotation with precisely the problem I alluded to at the end of the previous section: trying to understand the meaning of any particular representation of "mnemonics," given the varied types of memory techniques and devices that may legitimately be regarded as constituting such systems.

In terms of the concept of something "standing for" something else (see above), we could say, for instance, that a string tied around my finger stands for or "represents" the message I have stored in my memory, but we could also say that, as was true in early cuneiform, a cross inside a circle impressed on a clay tablet represented or stood for the logogram "sheep." Thus, we must ask, What was the nature of the "stand for" or representational relationship between an object in the world (e.g., a census figure, a royal genealogy, a character in a myth) and the knotted-string referent to that object in the khipu that is being proposed in this theory of khipu mnemonics?

The fact is, the concept of something "standing for" something else is extremely complicated. The idea of "standing for" is a central operation around which the great student and philosopher of signs Charles S. Peirce constructed his notion of "sign-action." As Peirce noted, "a sign, or representamen, is something which stands to somebody for something in some respect or capacity" (cited in Deledalle 2000: 72; my emphases). As the recent commentator on Peircean sign theory Gérard Deledalle notes: "`Stands for' is a perfect definition of the representamen [ca., sign] which `stands for' something which we do not know yet but that semiosis will possibly indicate in the course of the interpretive process" (2000: 73). Noting that Peirce defined the sign (in one of his many characterizations) as ". . . something by knowing which we know something more" (cited in Johansen 1993: 56), there is clearly, then, a problem with Rappaport and Cummins's characterization of features of khipu as "standing for" something to somebody while maintaining that, in fact, there are no conventionalized sign values incorporated in the khipu-that is, that interpreting these devices is not, after all, a semiotic process. I return at the end of this chapter to the interesting question of how the construction of khipu elements to stand for certain values could have led over time to the development of conventionalized signs. I give a more fulsome discussion of the general nature of khipu signs and sign systems in Chapter 6.

I would also question the meaning of the term "specified" in the above quotation from the work of Rappaport and Cummins. What are the principles of specification that may have been utilized in this mnemonic recording tradition? That is, on what grounds (e.g., hierarchical position? similitude?) might one have specified a connection between any given piece of memorized information and some specific feature(s) of a khipu? We do not find satisfactory answers to such questions in the otherwise very valuable and insightful works by Rappaport and Cummins on Andean literacies.

In regard to the point made earlier about topics involving statistical accounting that have received little attention in the literature by those who have discussed Andean literacies to date, I note that few of these scholars have discussed in any sustained way the numerical records or mathematical accounts concerning censuses, tribute records, and other such matters that are contained in the colonial documentation from the Andes, even though such topics represent the subject matter of a great many--if not the majority--of all Andean texts, whether in the khipu or in the written Spanish documents. For instance, in reading Rappaport and Cummins's otherwise thoughtful and insightful studies on literacy in the early colonial Andean world, one is left wondering, for instance, how the khipukamayuq, who spent the better part of every day of their lives studying knotted-string records of numerical accounts, may have thought about the mountains of documents produced by the Spaniards that contained essentially only numbers (i.e., using Hindu-Arabic numerals).

One topic relating to mathematical concerns that could potentially be of great interest and importance for studies of alphabetic literacy and numeracy is whether or not colonial Andean peoples would have developed traditions of viewing the actual numeral signs (1, 2, 3, . . .) as having iconic, symbolic values, as I have described for contemporary Quechua speakers in central Bolivia (Urton 1997: 221-231). The larger point here is that surely the experience of literacy on the part of these former Inka state record keepers would have been significantly different from that of the ordinary Andean villager, who seldom (if ever) attended to the intellectual and technical rigors of recording and carefully studying knotted-string records of numerical (and other?) values.

The issues raised above are emblematic of the absence of general theorizing on the nature of signs in the khipu to date. I return to this matter in Chapter 6, by which time we should be able to begin to lay out certain fundamental principles of a general khipu sign theory. To conclude this section, in my view, none of the arguments produced to date in support of the mnemonic interpretation of the khipu has specified with thoughtfulness or clarity how the various construction features of these devices might have been used by khipukamayuq as an "aid to the memory." In fact, it is hard to imagine how adherents of the mnemonic interpretive tradition might convincingly theorize concerning khipu mnemonic methods, given the fact that most adherents of this view have supposed that each of these devices was a unique product of the khipukamayuq who made and consulted it.

Scripts and Writing Systems

Defining what constitutes writing is a highly controversial, hotly contested matter (e.g., Boone and Mignolo 1994; Coulmas 1992; Coulmas and Ehlich 1983; Daniels and Bright 1996; DeFrancis 1989; Haas 1976; Harris 1986, 1995; Salomon 2001; Street 1984; Taylor and Olson 1995). Some scholars insist that so-called true writing should be limited to systems based on phonograms, which are the various types and levels of graphemes that denote the sounds of a language. Examples would include alphabetic, syllabic, and (at the margins) logosyllabic script systems. Logosyllabic systems are based on combined logogram plus syllabogram signing units; these include cuneiform and Egyptian and Mayan hieroglyphic writing. I referred to such scripts as "at the margins" of true writing because logograms have conventional semantic but not phonological value; examples would include such signs as 1, 2, 3, whose written forms, as keyed to spoken forms from a few exemplary languages, take the following forms: "one, two, three"; "uno, dos, tres"; or [in Quechua] "uj, iskay, kimsa."

Other students of writing seek to permit a wider range of types of scripts and signing systems--including nonphonologically based ones--within the fold of writing systems (e.g., Boone 1994: 15-17). Such definitions would, for instance, permit musical, dance, and mathematical notation systems, none of which signs phonetic values, to be defined as systems of writing (on such systems, see Aveni 1986; Drake 1986; Goodman 1976; Treitler 1981). Some (e.g., Arnold and Dios Yapita 2000: 46-49) have even suggested that signs such as the designs woven into textiles or scratched or painted onto ceramics should be defined as systems of writing. However, I think such signing devices are best classified as icons bearing conventional but highly abstract, context-specific meanings (see Mitchell 1987). Referring to such productions as writing, while perhaps satisfying what I would argue are essentially politically motivated programs or agendas promoting inclusiveness and multiculturalism (with which I am sympathetic), renders the concept of writing virtually meaningless and (more to the point) useless for analytical purposes.

Elizabeth Boone has argued persuasively that an adequate definition of writing must include provisions for both sound-based ("glottographic") and nonphonological, meaning-based ("semasiographic") sign systems (1994: 15-17; see also Sampson 1985: 29). The definition for writing that she derives on the basis of this relatively (but not absolutely) more inclusive set of considerations is: "...the communication of relatively specific ideas in a conventional manner by means of permanent, visible marks." It is unclear to me how nonspecific signs would have to be for them not to conform to Boone's stipulation that the ideas denoted must be "relatively specific." I am in agreement with the definition on this score if we reserve the term for phonological systems as well as those nonphonological glottographic systems based on highly conventionalized sign values (e.g., the logograms known as numeral signs, musical notations, algebraic and other mathematical notations, etc.) but exclude the designs and figures more commonly defined as iconography. On the other hand, since I maintain in this book that the khipu, whose signs were made up of three-dimensional string-and-knot configurations, constituted a system of communication of relatively specific ideas in a conventional manner, I argue that we do not need to retain the restriction in Boone's definition of the signs of writing to "marks"--by which I assume she means graphemes scratched, painted, or otherwise inscribed onto two-dimensional surfaces.

Given the above considerations, I would amend Boone's definition to say that writing is "the communication of specific ideas in a highly conventionalized, standardized manner by means of permanent, visible signs." Having arrived at this revised definition, however, I would also like to subscribe to the qualification that the forms of writing that accomplish the most highly specific level of denotation of ideas are those in which the signs of writing denote the sounds of the language community in question. As I noted earlier, these latter kinds of writing systems are ones that have often been referred to as "true writing." The qualifier is, of course, highly inflammatory and is consistent with the often ethnocentric way in which certain writers have discussed the evolution of (rather than differences between) different types of signing systems (see esp. Gelb 1963: 11-15).

I do not see any solution to this problem other than to drop the label "true writing" and maintain a straightforward distinction between glottographic (both phonologically and nonphonologically based) and semasiographic (non-language-utterance-based) sign systems and then to provide informed commentary on the uses to which various cultures put their respective record-keeping systems. This latter programmatic feature is especially important, because it is clearly the case that some societies have not had a need for complex, phonologically based script systems, and thus they did not invent them, while others did need such systems, so they did invent (or borrow) them. Therefore, the point on which differentiation between different types of signing/recording systems would turn (according to the perspective proposed here) is that of need, rather than intelligence.

Finally, I bring this introductory discussion of writing to an end by noting that although I refer at various places to the khipu communication system as a writing system, I use this designation in a generic sense. This is primarily for want of a better term, especially early in my exposition of a signing system in which (as I show later) the sign units signify--or are constituted as--the results of binary decision-making events and string/knot/color manipulations. The knots of khipu may all be assigned strings (i.e., series) of values in binary code. I argue that these coded series were read or interpreted on the basis of conventionalized values that were attached or assigned to particular coded sequences. As we will learn, the nearest analogy to this kind of "writing" is the process of writing binary number (1/0) coded programs for computers. These (computer) coded programs do not themselves constitute "writing"; rather, they provide the strings of electronic information units--e.g., 11100100/ 01000111/ etc.--whereby we can, for instance, type a text on a computer in alphabetic script, as was done with the text the reader is reading at this moment.

I give a complete overview of the theory of binary coding in the khipu at the beginning of Chapter 2. However, I hasten to assure the skeptical reader that khipu were not binary coding devices in some preternatural presaging of a form of technology (the computer) that has entered our own material culture only in the twentieth century. Rather, I show that the khipu was profoundly, legitimately, and of necessity--because it was based on the manipulation of threads in threedimensional space--based on binary coding.

Representations of Khipu Recording as "Writing"

In contrast to the mnemonic interpretive tradition outlined earlier, many students of the khipu over the years--beginning in the modern era perhaps with Julio C. Tello (1937; cited in Radicati di Primeglio 1964: 17-18)--have argued in favor of an interpretation that sees them more akin to a system of writing (see Arellano 1999; Ascher and Ascher 1997; Conklin 2002; Mignolo 1995: 84-86; Radicati di Primeglio 1964; Sempat Assadourian 2002; Urton 1994, 1998, 2002). Those who have adopted this alternative interpretation generally see the various construction features of the khipu as carrying and conveying what must have been widely shared logical and syntactical properties and semantic values, so that a trained khipukamayuq working in the state bureaucracy could pick up any khipu produced in the state-sanctioned khipu recording tradition and read or interpret the information in that record. The latter would have constituted an integrated system of knowledge, skills, and communicative practices that I believe would qualify, in the eyes of most theorists on writing and literacy, as a writing system (see Harris 1995: 21-32 on "integration" as a fundamental feature of literacy).

Various sources support the notion that the khipu was based on a shared recording tradition. For example, the chronicler Cristóbal de Molina ("el Cuzqueño") says the following with regard to the khipu records:

... they had a very cunning method of counting by strings of wool and knots, the wool being of different colours. They call them quipus, and they are able to understand so much by their means, that they can give an account of all the events that have happened in their land for more than five hundred years. 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. (cited and translated in Locke 1923: 36)

We also have a considerable amount of commentary on the khipu by one of the great Peruvian figures of Spanish-American letters, Garcilaso de la Vega. Garcilaso, a Quechua/Spanish mestizo who was born and raised in Cusco in the mid-sixteenth century and who claimed facility in reading the khipu, suggests that there was some degree of shared record keeping among khipu makers at the local level:

Although the quipucamayus were as accurate and honest as we have said, their number in each village was in proportion to its population, and however small, it had at least four and so upwards to twenty or thirty. They all kept the same records, and although one accountant or scribe was all that would have been necessary to keep them, the Incas preferred to have plenty in each village and for each sort of calculation, so as to avoid faults that might occur if there were few, saying that if there were a number of them, they would either all be at fault or none of them. (Garcilaso de la Vega 1966: 331; my emphasis)

Gary Urton is Dumbarton Oaks Professor of Pre-Columbian Studies at Harvard University, as well as a MacArthur Fellow (2001-2005).

"Urton's work is scholarly and painstakingly thorough and is a valuable contribution to our understanding of Inca inscription that makes good use of ethnographic and ethnohistorical work on the Andean region."
The Journal of the Royal Anthropological Institute

"This is by far the most important monograph on Andean systems of information registry since the Ashers' volumes in the late 1970s. Urton provides a platform for a whole new generation of studies."—Frank Salomon, Professor of Anthropology, University of Wisconsin–Madison

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