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khipu kód megfejtése

Az inka khipu kód: csomók, mint egy olvasón.

ANTHROPOLOGY: Cracking the Khipu Code
Science Magazine | 2003-06-13 | Charles C. Mann

Posted on 06/12/2003 6:09:19 PM PDT by Lessismore

Researchers take a fresh look at Incan knotted strings and suggest that they may have been a written language, one that used a binary code to store information In the late 16th century, Spanish travelers in central Peru ran into an old Indian man, probably a former official of the Incan empire, which Francisco Pizarro had conquered in 1532. The Spaniards saw the Indian try to hide something he was carrying, according to the account of one traveler, Diego Avalos y Figueroa, so they searched him and found several bunches of the cryptic knotted strings known as khipu. Many khipu simply recorded columns of numbers for accounting or census purposes, but the conquistadors believed that some contained historical narratives, religious myths, even poems. In this case, the Indian claimed that his khipu recorded everything the conquerors had done in the area, "both the good and evil." The leader of the Spanish party, Avalos y Figueroa reported, immediately "took and burned these accounts and punished the Indian" for having them. But although the Spanish considered khipu dangerous, idolatrous objects and destroyed as many as they could, scholars have long dismissed the notion that khipu (or quipu, as the term is often spelled) were written documents. Instead, the strings were viewed as mnemonic devices--personalized memorization aids with no conventionalized signs--or, at most, as textile abacuses. The latter view gained support in 1923 when science historian L. Leland Locke proved that the 100 or so khipu at the American Museum of Natural History in New York City were used to store the results of calculations.

For these reasons the Inca have often been described as the only major Bronze Age civilization without a written language. In recent years, however, researchers have increasingly come to doubt this conclusion. Many now think that although khipu probably began as accounting tools, they had evolved into a writing system--a kind of three-dimensional binary code, unlike any other on Earth--by the time the Spanish arrived. "Most serious scholars of khipu today believe that they were more than mnemonic devices, and probably much more," says Galen Brokaw, an expert in ancient Andean texts at the State University of New York, Buffalo.

Yet the quest to understand khipu faces a serious obstacle: No one can read them. "Not a single narrative khipu has been convincingly deciphered," laments Harvard University anthropologist Gary Urton, who calls the situation "more than frustrating." And so Urton, spurred by new insights gained from textile experts, is now preparing the most sustained, intensive attack on the khipu code ever mounted. In a book to be released next month, Signs of the Inka Khipu (University of Texas Press), he has for the first time systematically broken down khipu into their constituent elements. He is using that breakdown to create a khipu database to help identify patterns in the arrangement of knots. Just as Maya studies exploded in the 1970s after researchers deciphered Maya hieroglyphs, Urton says, breaking the khipu code could be "an enormous potential source of insight" into the lives and minds of the still-mysterious Inca, who in the 16th century ruled the largest empire on Earth.

Binary code?

All known writing systems used for ordinary communication employ instruments to paint or inscribe on flat surfaces. Khipu, by contrast, are three-dimensional arrays of knots. They consist of a primary cord, usually 0.5 to 0.7 centimeters in diameter, to which are tied thinner "pendant" strings--typically more than 100 and on occasion as many as 1500. The pendant strings, which sometimes have subsidiary strings attached, bear clusters of knots. The result, as George Gheverghese Joseph, a mathematics historian at the University of Manchester, U.K., has put it, "resembles a mop that has seen better days."

According to colonial accounts, Incan "knot-keepers"--elite bureaucrats called khipukamayuq--parsed the knots both by inspecting them visually and by running their fingers along them Braille-style, sometimes accompanying this by manipulating stones. For example, to assemble a history of the Inca, in 1542 colonial governor Cristóbal Vaca de Castro apparently summoned khipukamayuq to "read" the strings. Spanish scribes recorded their testimony but did not preserve the khipu; indeed, they may have destroyed them.

Locke showed that the numerical khipu were hierarchical, decimal arrays, with the knots used to record 1's on the lowest level of each string. Other knots were tied on successively higher levels in a decimal "place value" system to represent 10s, 100s, 1000s, and so on. "The mystery has been dispelled," exulted archaeologist Charles W. Mead after Locke's discovery. "We now know the quipu for just what it was in prehistoric times ... simply an instrument for recording numbers."

But Locke's rules did not decode all of the estimated 600 khipu that survived the Spanish. Nor did they detail what objects were being accounted for in these records. According to Cornell University archaeologist Robert Ascher, about 20% of khipu are "clearly nonnumerical." In 1981, Ascher and his mathematician wife, Marcia, published a book that reignited the field by intimating that these "anomalous" khipu may have been an early form of writing.

The Aschers focused mainly on khipu knots. But in 1997, William J. Conklin, a research associate at the Textile Museum in Washington, D.C., suggested that knots were only part of the khipu system. "When I started looking at khipu," says Conklin, perhaps the first textile specialist to investigate them, "I saw this complex spinning and plying and color-coding, in which every thread was made in a complex way. I realized that 90% of the information was put into the string before the knot was made."

Taking off from this insight, Urton proposes that khipu makers made use of the nature of spinning and weaving by assigning values to a series of binary choices (see diagram), including the type of material (cotton or wool), the spin and ply direction of the string (which he describes as "S" or "Z" after the "slant" of the threads), the direction (recto or verso) of the knot attaching the pendant string to the primary, and the direction of slant of the main axis of each knot itself (S or Z). As a result, he says, each knot is a "seven-bit binary array," although the term is inexact because khipu had at least 24 possible string colors. Each array encoded one of 26 x 24 potential "information units"--a total of 1536, somewhat more than the estimated 1000 to 1500 Sumerian cuneiform signs and more than twice the approximately 600 to 800 Egyptian and Maya hieroglyphic symbols. In Urton's view, the khipu not only were a form of writing, but "like the coding systems used in present-day computer language, [they were] structured primarily as a binary code."

If Urton is right, khipu were unique. They were the world's sole intrinsically three- dimensional "written" documents (Braille is a translation of writing on paper) and the only ones to use a binary system for ordinary communication. In addition, they may have been among the few examples of "semasiographic" writing: texts that, like mathematical or dance notation but unlike written English, Chinese, and Maya, are not representations of spoken language. "A system of symbols does not have to replicate speech to communicate narrative," explains Catherine Julien, a historian of Andean cultures at Western Michigan University in Kalamazoo.

Knotted string communication, however anomalous to Euro-American eyes, has deep roots in Andean culture. Khipu were but one aspect of what Heather Lechtman, an archaeologist at the Massachusetts Institute of Technology's Center for Materials Research in Archaeology and Ethnology, describes as "a technological environment in which people solved basic engineering problems through the manipulation of fibers." In Andean cultures, Lechtman says, textiles--ranging from elaborately patterned bags and tunics to missile-hurling slings and suspension bridges--were "how people both communicated messages of all sorts and created tools." Similarly, Urton explains, binary oppositions were a hallmark of the region's peoples, who lived in societies "typified to an extraordinary degree by dual organization," from the division of town populations into "upper" and "lower" moieties to the arrangement of poetry into dyadic units. In this environment, he says, "khipu would be familiar."

But this grander view of khipu as written narrative also has its critics. "Due to cultural evolutionary theory, people have decided that cultures are not really any good unless they have writing," says Patricia J. Lyon of the Institute of Andean Studies in Berkeley, California. "People feel this great need to pump up the Inca by indicating that the khipu were writing." Agreeing with the 17th century Jesuit chronicler Bernabé Cobo, Lyon believes that khipu "were mnemonic devices, no matter what you dream up."

Even some of Urton's supporters are cautious about his interpretation. Conklin, for instance, agrees that the khipu were charged with meaning, but he worries that the analogy to computer language may not fit. "The Andean concept of duality is different than ours," he says. Whereas each 1 or 0 in a binary display is completely independent, the Andean dualities "are like the ebb and flow of a tide: opposing, interacting aspects of a single phenomenon." In his view, understanding khipu will require finding "a way other than our independent zero and one to express Andean dualism." Still, he says, Urton's work "is the first attempt to push khipu forward since Leland Locke."

Seeking a Rosetta stone

One way to settle the debate decisively would be to find a written translation of a khipu to another language--an Incan Rosetta stone. In 1996, Clara Miccinelli, an amateur historian from the Neapolitan nobility, caused a stir by announcing that she had unearthed just such a find in her family archives: an explicit translation into Spanish of a khipu that encodes a song in Quechua, the Incan language, which is still spoken today. But because the same collection of documents also contains sensational claims about the Spanish conquest, many scholars have questioned their authenticity. Miccinelli has thus far refused to let researchers around the world freely examine the documents, although she did allow an Australian lab to use a mass spectrometer to test the khipu that accompany them. The results, published in 2000, date the khipu to between the 11th and 13th century. According to Laura Laurencich Minelli, an Andeanist at the University of Bologna working with the Miccinelli documents, the early age could be explained by the Andean tradition of weaving important khipu with old thread "charged with the strength of the ancestors."

Because they cannot examine the documents, most researchers are "strategically ignoring" them for now, says Brokaw, and are tackling khipu using less controversial means. Urton and mathematician and database manager Carrie Brezine intend to have their khipu database, which is funded by the U.S. National Science Foundation, running this fall and will eventually put it online. Their database, a successor to one set up by the Aschers at Cornell, will let scholars search for patterns across most of the 600 surviving khipu.

At the same time, Urton and other khipu hunters are searching for their own Rosetta stone: a colonial translation of a known khipu. For example, some Spanish documents from Peruvian Amazonia are thought to be transcriptions of khipu, 32 of which were recently found in the area. No definitive match has yet been made between a document and the newly discovered khipu, but Urton has uncovered some suggestive clues. He is now searching archives in Peru and Spain for more documents--a quest, according to Western Michigan's Julien, that "has a chance of bearing fruit." The 40-plus Incan provinces had similar, overlapping records, she notes. "Information from one province could easily be found in another form in another [province]." If Urton or some other scholar can find a match, she says, "we may be able to hear the Incans for the first time in their own voice."


Science 12 August 2005:
Vol. 309. no. 5737, pp. 1065 - 1067
DOI: 10.1126/science.1113426



Khipu Accounting in Ancient Peru

Gary Urton and Carrie J. Brezine

Khipu are knotted-string devices that were used for bureaucratic recording and communication in the Inka Empire. We recently undertook a computer analysis of 21 khipu from the Inka administrative center of Puruchuco, on the central coast of Peru. Results indicate that this khipu archive exemplifies the way in which census and tribute data were synthesized, manipulated, and transferred between different accounting levels in the Inka administrative system.

Department of Anthropology, Harvard University, Cambridge, MA 02138, USA.

Tribute in the Inka state was levied in the form of a labor tax. Each "taxpayer" (state laborer) was required to work a specified number of days each year on state projects. Using data recorded in khipu (knotted-string devices used for bureaucratic recording and communication), Inka accountants assessed tribute levels and assigned tasks to different numbers of local workers. At the lowest, local level of the administrative hierarchy, tributaries were grouped into five accounting units of 10 members each. One member of each of these groups of 10 would have served as Chunka Kamayoq ("organizer of 10"). Five such groupings would make a unit of 50 tribute payers, under the authority of a Pichqa-Chunka Kuraka ("lord of 50"). Two groups of 50 would be combined into a unit of 100 tributaries led by a Pachaka Kuraka ("lord of 100") and so on up the hierarchy.

Near the top of the decimal administrative hierarchy were the heads of the approximately 80 provinces, the officials of which were called T'oqrikoq. Each provincial official was under the direction of the appropriate Lord of the Four Quarters; these four lords served directly under the Inka king in Cusco. The governor of each province was required to keep a copy of khipu accounts so that "no deception could be practiced by either the Indian tribute payers or the official collectors" (1).

A primary question is how did information move between adjacent levels of this hierarchical administration? The instructions of higher-level officials for lower-level ones would have moved, via khipu, from the top of the hierarchy down. This information would be partitive in nature; for instance, assignments made to 1000 tribute payers would be broken down into two groups of 500, each of which would be decomposed into five groups of 100, and so on. In the reverse direction, local accountants would pass data regarding accomplished tasks upward through the hierarchy. In that direction, information at each level would represent the summation of accounts from the level immediately below. These accumulating data would eventually arrive in the hands of the Cusco accountants, where the highest level of accounting went on. Here we present an analysis of a set of khipu from Puruchuco that are linked hierarchically in such a relationship of summation and partition.

The archaeological site of Puruchuco is located on the south bank of the Rimac River, about 11.5 km northeast of the center of Lima, within the present-day district of Ate. Puruchuco is a roughly rectangular compound with high surrounding walls made of tapia (pounded adobe) construction. Around and in some cases abutted to the palace of Puruchuco were several smaller constructions. The cache of khipu was found under the floor of one of the smaller attached buildings. From its location, Mackey surmised that this building was the house of a khipu-keeper (khipukamayuq) who served the lord of the palace (2). Field notes from the day on which the khipu were discovered state that they were found inside a semi-ovoid urn covered by a small gourd. There were 21 khipu and several loose pendant strings (3).

What we term the Puruchuco "accounting hierarchy" pertains to 7 of the 21 khipu samples found together in the urn. Though not included in this analysis, several other khipu may provide supporting documentation to these seven. The seven khipu are related in a hierarchical arrangement of three interconnected levels, designated levels I, II, and III, as shown in Fig. 1. Two of the seven khipu (UR63 and UR73) were on level I, the base; three khipu were on the second level [UR64, UR68, and 9 (4)]; and two (UR67 and UR66) were on level III.

 Fig. 1. The accounting hierarchy from the archive of Puruchuco. [View Larger Version of this Image (42K GIF file)]
The two samples at the top of the hierarchy, UR66 and UR67, were rolled up together into a single bundle. These two khipu bear identical numerical values and string colors that seem to be a subtle transformation from one to the other.

There are two principal aspects of the Puruchuco accounting hierarchy. First, khipu on the same level match or closely match: They display identical or similar numerical sequences and color patterning. This, we argue, was the checks-and-balances aspect of the accounting hierarchy. Second, values on khipu sum upward and are subdivided downward: The numerical values of certain groupings of strings (to be defined below) on the two khipu on level I sum to values tied onto certain groupings of strings on the three khipu on level II, and the numerical values of certain groupings of strings on the three khipu on level II sum to the values on the two khipu on level III. Or, moving down the hierarchy, values on strings at higher levels are partitioned among groupings of strings on the next lowest level.

Through cord color and spacing, each of the seven khipu is organized into different numbers of subunits. Khipu on level I decompose into six subunits; those on level II contain three subunits (plus what we call "introductory segments"); and the two khipu on level III have only one unit (plus introductory segments). Inside these subunits, the strings are further subdivided by a combination of spacing between strings and/or by the repetition of color patterning in groups of strings. The general color pattern is a four-string seriation or sequence of colors (such as dark brown, medium brown, light brown, and white) repeated multiple times (5, 6). The numerical values of the cords vary in magnitude in accordance with the color, with the four strings of each color-seriated set generally increasing in size through the sequence.

An example of summation upward, between UR68 on level I and UR63 on level II, is given in Fig. 2. UR63 is organized by spacing and color seriation into six pendant string groupings, labeled a to f. The number of strings in each group is shown in brackets at the bottom of the columns. The six columns comprise (i) three sets of (5 x 4 =) 20 strings organized into five groups of four color-seriated strings; (ii) two sets of (3 x 4 + 2x 3 =) 18 color-seriated strings; and (iii) one set of (3 x 4 + 3=) 15 color-seriated strings. The meandering dotted lines at the tops and bottoms of the columns of UR63 in Fig. 2 show how this sample is to be reassembled into its proper linear arrangement. The numerical values of string groupings in UR63 sum to values recorded on the middle of the three subunits of UR68. The color-seriated strings of UR63 are aligned across the six segments, and these groupings are aligned with the similarly color-seriated grouping of (5 x 4=) 20 strings in the central subdivision (strings 34 to 53) of khipu UR68. Summing across the aligned strings of UR63 results in totals equal or close to those recorded on the depicted section of UR068. The values knotted into the cords of UR68 are reported on the right; any number between parentheses immediately to the left of these is the actual sum of values on the strings of UR63 at that position. The parenthetical numbers represent values that should have been recorded if the relationship between UR63 and UR68 was a matter of strict addition. The presence of several close, rather than exact, matches suggests that there was some degree of flexibility allowable in the accounting relationship between these two levels.

 Fig. 2. Numerical and color correlations between khipu UR63 and the central section of UR68. [View Larger Version of this Image (26K GIF file)]
Continuing the summing upward, we next consider khipu UR68 (level II) and UR67 (level III). Their relationship is illustrated in Fig. 3. UR68 is disassembled into its three color-seriated subdivisions (labeled A to C), which are shown aligned with the similarly color-seriated string groupings of UR67. Figure 3 shows 20 strings in all subunits.

 Fig. 3. Numerical and color correlations between khipu UR68 and UR67. [View Larger Version of this Image (19K GIF file)]
The summations between UR68 and UR67 are more exact than those between UR63 and UR68. Setting aside the broken string in UR67, the values diverge in only two instances, and in each case the discrepancies are small: 2904 instead of 2908 and 161 instead of 162. The variance present in the connection between levels I and II has been considerably reduced between levels II and III.

Pendants between dotted lines in Fig. 1 are implicated in the summation/partition relationship. The pendants on level III outside of the dotted lines, and those to the left of the dotted lines that protrude from the tops of the khipu on level II, form introductory segments. The dotted lines in Fig. 1 encompass all the pendants on level I khipu but only the middle subunit of level II khipu. That is, complete summation of level I khipu accounts for only a portion of the values recorded on khipu on level II. The other values on level II khipu are not accounted for by the currently known level I khipu UR63 and UR73. There may have been four additional level I khipu, with the information for these two additional subunits on level II. One pair would have summed to the leftmost subunits on level II, whereas the other would have produced sums recorded on the right subunits. Except for the introductory segments, all strings on level III are involved in the summation relationship.



It appears that the original structure of the Puruchuco accounting hierarchy contained six paired khipu on level I, whose values were summed to produce those on the three subunits of the three khipu on level II, whose subunits in turn were summed and recorded on the two khipu on level III. Information was either being funneled and synthesized upward or subdivided and distributed downward among the three levels of khipu.

We assume that the Puruchuco accounting hierarchy was a set of records for use both within and outside the administrative center. Khipu on level III could represent either a set of instructions issued to the lord of Puruchuco from the provincial governor or reports on local Puruchuco resources to be sent to the provincial governor. In either of these scenarios, one of the requirements would have been that the khipu bear an indication of their destination or origination. If numerous khipu were coming into a central archive for storage or were being dispersed from that archive to disparate places, it would have been helpful, if not essential, to have place identifiers encoded within each khipu. We suggest that the introductory segments on level II and III khipu represented just such identity labels.

The numerical values knotted onto strings within the introductory segments on level II and III khipu all contain arrangements of just three figure-eight knots tied onto three separate strings. Figure-eight knots on khipu normally signify the numerical value one. We hypothesize that the arrangement of three figure-eight knots at the start of these khipu represented the place identifier, or toponym, "Puruchuco." We suggest that any khipu moving within the state administrative system bearing an initial arrangement of three figure-eight knots would have been immediately recognizable to Inka administrators as an account pertaining to the palace of Puruchuco.


Why don't level I khipu bear introductory segments? Perhaps UR63 and UR73 were not intended to travel away from Puruchuco; instead, they may have been local accounts, drawn up by the resident khipukamayuq for accounting purposes within the palace. If the seven khipu in Fig. 1 register demands for service received from outside Puruchuco, meaning that if the relation among them is one of partition, then the level I khipu would have represented the reorganization of the mandate from outside in relation to the availability of resources at the local level. In this scheme, level I khipu would have pertained only to local accounting matters, and it would have been unnecessary to attach the place identifier. However, if the overall relationship is one of summation, and these khipu were prepared as a report on local conditions for dispatch outside Puruchuco, then level I khipu would represent the raw tables of local information that served as the foundation for constructing level II and III khipu. Level III khipu, the summary reports, would have been sent to a distant administrative center.

We suggest that khipu may have contrasting number qualities depending on whether they represented instructions coming from the state administration to a local accounting center or were records produced within a local accounting center with regard to existing community resources. In the first circumstance, we suspect that khipu values would have tended to be even decimal values or calculations of values in standard proportional shares. If a khipu account was compiled from within some local administrative center to be sent upward to higher level officials, counts of resources could be expected to have reflected the vagaries of the natural distribution of items in society. Such numbers are less likely to be whole and rounded or perfectly proportional.

We believe that the Puruchuco archive is the first known example indicating how information moved both up and down the Inka administrative hierarchy. There is insufficient evidence to determine whether the khipu are related through data partition or summation; however, careful study of the Puruchuco and other khipu archives may provide the foothold needed for addressing the most difficult question facing students of the Inka khipu: How did the khipu-keepers of the Inka administrative system record the identities of objects—people, animals, produce, manufactured goods, etc.—in the three-dimensional forms of their knotted-string records (7)?

References and Notes

  • 1. G. de la Vega, El Inca, Royal Commentaries of the Incas (Univ. of Texas Press, Austin, TX, 1966).
  • 2. C. Mackey, thesis, University of California, Berkeley (1970).
  • 3. Thanks to Julio Tello Solis for his transcription (10 July 2004) of the notes from the excavation field reports at Puruchuco, here translated by Urton: "9 August, 1956—The work consisted, as over the past three days, in removing `fill,' or dirt from the upper part of sector B to fill a pit in Platform A... In the zone of extraction (Sector B, upper part) of the fill the workman Lizama encountered a narrow-necked urn (cantaro), semi-ovoid in form, covered with soot (hollín) and with an applique on the outer body in the form of a serpent; its [i.e., the urn's] mouth was covered by a small lagenaria [bottle gourd]; in the interior there were found 10 khipu of regular size, 3 of which had red/orange/yellow tassels, 11 medium sized ones, and several loose pendant strings, all in a good state of preservation."
  • 4. Sample 9 was in the Puruchuco museum when Carol Mackey studied this collection in the 1960s. When we restudied the Puruchuco khipu archive in the summer of 2004, 9 was no longer in the collection. Museum personnel could not tell us what had become of this sample.
  • 5. C. Radicati de Primeglio, La `Seriación' como posible Clave para Descifrar los Quipus Extranumerales (Biblioteca de la Sociedad Peruana de Historia, Lima, Peru, 1964).
  • 6. F. Salomon, The Cord Keepers: Khipus and Cultural Life in a Peruvian Village (Duke Univ. Press, Durham, NC, 2004), pp. 252–255.
  • 7. The Khipu Database project, located in the Department of Anthropology, Harvard University, is described fully on the project Web site at http://khipukamayuq.fas.harvard.edu/.
  • 8. We thank L. F. Villacorta Ostolaza and the staff of the Museo de Sitio Puruchuco–Arturo Jiménez Borja: Bullón, Díaz, and Solis. We thank NSF (grant BCS-0408324); the Dumbarton Oaks Foundation; and the Faculty of Arts and Sciences, Harvard University, for support; and the John D. and Catherine T. MacArthur Foundation for G.U.'s MacArthur Fellowship.
Received for publication 11 April 2005. Accepted for publication 13 July 2005.

Unraveling Khipu's Secrets
Charles C. Mann (12 August 2005)
Science 309 (5737), 1008. [DOI: 10.1126/science.309.5737.1008]
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