Khipu PDF - The Khipu in Tawantinsuyu

The Khipu in Tawantinsuyu Manuel Medrano In AD 1533, during the early phases of the Spanish conquest of the Andes, a conquistador named Hernando Pizarro instructed his men to plunder a storehouse along the Inkas’ royal road. As they did so, Pizarro noticed...

The Khipu in Tawantinsuyu Manuel Medrano In AD 1533, during the early phases of the Spanish conquest of the Andes, a conquistador named Hernando Pizarro instructed his men to plunder a storehouse along the Inkas’ royal road. As they did so, Pizarro noticed a curious practice: the native storehouse keepers, who held bundles of strings in their hands, removed certain knots and re-knotted them elsewhere to record the changing inventories. What were these unfamiliar devices? How did they work? And what can they teach us about Tawantinsuyu, the expansive empire of the Inkas? The object Pizarro witnessed was a khipu (also spelled quipu or kipu), a knotted-string device used by Andean peoples for recording both numerical and nonnumerical information for at least 1,000 years (c. 950–1950 AD; see Figure 1). Khipu use reached its apex during the time of the Inkas, who utilized plied, multicolored cords for registering everything from census records and storehouse inventories to (reportedly) histories, genealogies, and songs. A specialized class of cord-keepers called khipukamayuqs (pronounced as kipukamayokkus, khipu specialists) maintained khipus of interest to high-level Inka administrators, including numerical specimens that tracked demographic and labor information in various accounting hierarchies. Non-Inka individuals produced khipus as well; the rich diversity of these objects has prompted comparisons to the modern concept of “genres.” Today, some 1,400 khipus survive in museums and private collections. Others are kept in Andean villages, where they are considered sacred patrimony by community members. Dozens more have been excavated by archaeologists in recent decades. Yet khipus, the primary sources of the Inkas, remain only partially deciphered. Surveying their storied history – and ongoing attempts to read them – is this essay’s dual focus. 1 == Figure 1: Inka-style Khipu Fragments in the Museum der Kulturen, Basel, Switzerland == Several important clarifications will serve as our entry point to exploring these questions. First, khipus were not calculation devices or abacuses. When they did record numbers, the values were produced by an accompanying grid-like device called a yupana, whose use remains little-understood. Similarly, khipus were not like computer binary code, in which an underlying series of independent 0s and 1s produces meaning; the multiple components of a khipu were interdependent and interacted in complex ways, rather more like a flow-chart or diagram. Our inability to find an adequate metaphor to describe the khipu reflects its interdisciplinary nature: it combined elements of what we today call reading, writing, and mathematics in a single medium. And a complex medium it was – current estimates suggest that a single khipu string could take between 1.65 and 8 million configurations. A khipu with even three attached strings could exhibit 365 billion different possible forms, according to one 1970s researcher. This is not to mystify the khipu’s expressive capacity – only a small subset of these potential combinations would have been in use on any given sample – but it does reaffirm the importance of considering the khipu in its full range of variations and styles. 2 At the same time, most surviving khipus have a consistent shape, which researchers generally refer to as “Inka-style” (Figure 2). On Inka-style khipus, between 1 and over 1,000 pendant cords hang down like a fringe from a horizontal primary cord. The “reading” direction of the khipu depends on its orientation, but this is conventionally done from left to right when (in unbroken samples) the longer, dangling end of the primary cord can be oriented to the viewer’s right side. On some khipus, vertical top cords are tied in an opposite direction to the pendant cords. Both pendant and top cords can themselves have additional, subsidiary cords attached. Finally, most attached strings, whether top, pendant, or subsidiary, are knotted with one of three types of knots. In the early 20th century, L. Leland Locke, an American mathematics teacher and historian of science, deciphered the meaning of these knots, showing that they record numbers in a decimal (base-10) system: simple overhand knots register tens, figure-eight knots register the value “1,” and long knots register the values 2–9, depending on how many times the string is twisted around itself while tying them (Figure 3). Thus, the number 2,035 is indicated with two overhand knots in the thousands’ place, no knots in the hundreds’ place, three overhand knots in the tens’ place, and a long knot with five turns in the ones’ place. == Figure 2: Structure of an Inka-style Khipu == 3  == Figure 3: Numerical Khipu Knots == Other elements of the Inka-style khipu remain relatively opaque. Most khipu cords appear to be made of cotton, though examples made of other vegetal material, animal fiber, and even human hair have been identified. The cords exhibit different color profiles, including solid, mottled, "barber-pole" (cords composed of two or more different-colored fibers or threads in a spiral formation), and color-change varieties, many of which were produced with natural dyes (Figure 4). Other elements of the khipu are binary in nature, including the attachment knots with which pendants are affixed to the primary cord (either tied toward or away from the viewer), the ply of the strings (either “S” or “Z,” like the diagonal axis of each letter), and the horizontal and vertical orientation of the numerical knots (also “S” or “Z”, with long knots simultaneously appearing in either an “up” or “down” direction). Bright threads were sometimes inserted in or wrapped around parts of the khipu, potentially as markers or navigational aids. 4  == Figure 4: Solid, Mottled, Barber-Pole, and Color-Change Pendant Cords in an Inka-style Khipu== Chronology Despite their popular association with the Inkas, the khipu was not an Inka invention. In fact, the Inka khipu tradition represents less than 15% of its known lifespan in the Andes – the khipu’s appearance in Tawantinsuyu was both derivative of pre-Inka khipu practices and forebearer to postconquest ones. In this regard, then, we can speak of several known khipu “traditions” (Figure 5). Before the Inkas, and from at least the tenth century AD, the Wari Empire (ca. AD 700-1000) produced khipus for its own internal administration. Several distinguishing characteristics have been identified from the roughly 40 surviving examples of Wari khipus. These include the use of bright, tube-like thread wrappings, which have been hypothesized to indicate nonnumerical and/or categorical information; the exclusive use of overhand, Z-knots; and a smaller overall structure, rarely with more than a few pendants. Wari khipus remain almost completely undeciphered, with experts disagreeing over whether its knots fit a binary (base-2), quinary (base-5), or decimal (base-10) numerical system. Only a few Wari khipus have been discovered under controlled archaeological conditions. 5  == Figure 5: Khipu “Traditions” == The Late Intermediate Period (LIP; AD 1000-1470), the several-century gap between the disintegration of Wari around 1000 AD and the rise of the Inkas, presents a conundrum to khipu researchers. Despite rich khipu traditions attributed to Wari and the Inkas, few if any khipus have been confidently assigned to the LIP; those that have been were radiocarbon dated. LIP khipus have not yet been discovered with firm archaeological context, and the cultures or peoples that made them remain largely anonymous. These shortcomings notwithstanding, a range of continuities seem evident between Wari and both Inka and colonial khipus. Most obviously, the canonical, Inka-style structure of a horizontal primary cord with attached pendants is also observed in Wari and LIP specimens. The multicolored pendant strings of Inka and post-Inka khipus, both dyed and naturally colored, may have descended from the colorful thread wrappings of Middle Horizon fame. The period’s characteristic overhand knots were incorporated into an expanded register of Inka numerical knots that survived at least into colonial times, if not later. The persistence of these characteristics was both propelled and constrained by Spanish colonial institutions. Propelled, in that Andeans created khipus to measure malfeasance by colonial administrators and other individuals – among other information – under the encomienda labor system (here, it refers to a grant of the Spanish Crown to reward a Spanish 6 conqueror with the labor of a particular group of non-Christian Andean people. The system often devolved into a type of de facto, communal slavery). The cross-comparison and reporting of such accounts in both official and unofficial settings facilitated the reproduction of complex, local-regional practices of khipu literacy across multiple generations. For subsequent decades and centuries, colonial documentation identifies information read unproblematically from khipus; the unexpected consequences of this implicit condonement surfaced by the mid-late 18th century, when khipus were reportedly used for the planning of anti-colonial rebellions in the Andean highlands and Bolivian altiplano (high plateau). In contrast, other colonial practices constrained the persistence of khipu literacy, perhaps most visibly in a decree of the 1583 Third Lima Council that called for the destruction of khipus recording the “ancient superstitions” of the Indians. In at least one instance, surviving documentation describes a khipu confiscated and burned at the hands of Spanish administrators. Yet the extent of this search-and-destroy operation is a topic of lively debate today, since Catholic indoctrination more broadly in the 17th century would involve the imposed requirement of khipus for catechesis, including as confessional aids and rosaries. Hybrid khipu-alphabetic texts known as khipu boards recorded church attendance in some Indian parishes from at least the 16th century onward. Funerary khipus, which record Christian prayers and are still wrapped around the waists of deceased community members in some villages, may be just as old a tradition. Following Peruvian independence in 1821, khipus appear most frequently in agro-pastoral and ritual contexts, often in a simplified construction in which cord and knot thickness indicate powers of ten. More recent research has employed both ethnographic and historical methods to document the high degree of heterogeneity in modern khipu-making, which seems to have otherwise seen little standardization in color, fiber, or structure. Nonetheless, 7 insights into these varied practices among today’s communities offer valuable clues as to the possible functions and recording conventions of ancient specimens. Function For contemporaneous evidence of Inka khipu use, researchers look to surviving archaeological specimens, as well as written descriptions of khipus in chronicles and legal- administrative records produced shortly following the Spanish conquest. In the first case, khipus recovered from controlled archaeological contexts enable more confident assessments of former use. These come predominantly from more arid coastal sites, as the vast majority of Inka khipus from the highlands seem to have disintegrated in the wetter climate. At Inkawasi, an Inka staging facility in the Cañete Valley, dozens of khipus have been recovered since 2013 from specific locations in the site’s storehouse. Some were found underneath piles of peanuts, black beans, and chili peppers, leading archaeologists to hypothesize that these khipus recorded the accession and deposition of these items in the storage complex. In addition, many of the Inkawasi khipus exhibit closely matching numerical values, which suggests that a type of double-entry bookkeeping was in use by khipu accountants there. The identity of these accountants is a topic of ongoing disagreement. At Inkawasi, significant concentrations of non-Inka ceramics have led archaeologist Alejandro Chu to suggest that its khipukamayuqs were in fact local ethnic elites, rather than Inkas. Eleven khipus discovered in 2017 at the architectural complex of Huacones-Vilcahuasi, also in the Cañete Valley, have informed a similar hypothesis. A rare yupana was uncovered in a nearby sector to the Huacones khipus, which Sergio Barraza Lescano and colleagues interpret as the remains of an administrative center run by khipu-wielding local (non-Inka) elites. Increasingly, research on Inka khipus found at provincial sites has reinforced the narrative that once the Inkas conquered and incorporated the ethnic polities of the Peruvian coast, they often opted to leave 8 in place local calculation and accounting regimes rather than superimpose their own. Designated individuals literate in both local and Inka khipu techniques may have helped to “translate” local khipu accounts into the summary khipus that would have been transmitted to Inka overseers. One potential example of such practices is a set of administrative khipus discovered at Puruchuco, an archaeological site near the city of Lima. A bundle of specimens found together in an urn – a sort of khipu “archive” – have been shown to record numbers that can be arranged in a three-level hierarchical relationship. Adding together strings from the lowest level khipus produces values recorded on the middle tier khipus, which in turn are summed on the uppermost level. Some of the upper-level specimens have repeated figure-eight knots on their leftmost strings, which some researchers have interpreted as a nonnumerical label for the toponym “Puruchuco.” If supported by further research, this would have allowed receiving authorities to identify the origin of the specimens at a glance, reflecting organizational practices within the Inka administrative hierarchy. At the same time, more difficult has been the interpretation of khipus discovered in Inka and Late Horizon mortuary contexts. Why bury a khipu with a deceased individual? Are there commonalities in style or form that might suggest a shared practice? It is difficult to speak with certainty, since most khipus from graves were extracted in the late 19th and early 20th centuries, often by foreign explorers, with few if any records of their discoveries produced. Among those with modern documentation, however, a variety of contexts have been observed. Discoveries of khipus associated with discrete individuals remain relatively – and somewhat surprisingly – uncommon. One example comes from the port settlement of Armatambo, also near Lima, where two adult individuals were interred in a bent position. A deteriorated reed sewing kit was found below one adult, while a khipu was found underneath 9 the hand of the other individual, who appears to have been buried holding it. Their identities are unclear. More common in past decades has been the discovery of khipus in collective burials. The excavation of a different burial at Armatambo revealed eight khipus within an assemblage of remains of at least ten individuals, who have been interpreted as administrative officials. More recently, a cache of 28 khipus and khipu fragments has been uncovered at Huaycán de Cieneguilla, in the Lurin Valley just south of Lima. In this case, the specimens were rolled up in an offering packet, which was placed in a tomb that contained the mixed remains of at least six individuals, interpreted as a curaca-khipukamayuq (another category of Inka official; curaca refers to a local ethnic leader) along with his sacrificed servants and assistants. However, the khipus and human remains were not placed in direct contact with one another. This is in some contrast to an infant funerary bundle discovered at Cerro Colorado (Huaura Valley, on the north-central coast of Peru, north of Lima) in 2014. What appears to be an unknotted khipu was laid on the infant’s chest, which has led archaeologist Peter van Dalen Luna to interpret the individual as a future khipukamayuq buried with his work tool. A final class of archaeological khipus includes specimens that are reported to have come from the same location, but otherwise lack clear documentation. The largest known source of such khipus is Pachacamac, a well-known pre-Inka and Inka pilgrimage site just south of Lima, which has yielded over 90 inventoried specimens to date. Many khipus from the site are today scattered across collections, sometimes with only an affixed, early 20th century tag reading “Pachacamac” providing its supposed source. The Pachacamac corpus is an important set of evidence for khipu researchers, since many of the specimens would have been manufactured elsewhere and brought to the site by visitors making ritual offerings. They might thus serve as a proxy for the diversity of khipu traditions across Tawantinsuyu. On initial inspection, there are different color patterns, construction styles, and other 10 characteristics apparent within the corpus, which might suggest a significant degree of regional khipu variation. Nonetheless, other researchers have interpreted the same specimens in the opposite way. They point to the samples’ consistently disproportionate use of knots tied in the “Z” direction as evidence for a high degree of khipu standardization across the Empire. Ultimately, future studies will need to juxtapose such continuities and divergences to discriminate between hypotheses in a more concrete way. The other type of evidence commonly cited in the study of Inka khipus comes from the postconquest documentary record. Best known in this regard are the writings of the colonial chroniclers, who from the mid-late 16th century onward produced histories of the Inkas that cited khipus in various contexts. Some interviewed former Inka khipukamayuqs, while others claimed to be literate themselves in reading khipus, describing recordings conventions that have often found limited support in modern research. For example, multiple chroniclers describe a one-to-one correspondence between cord colors and information categories: red for warriors, black for time, purple for curacas and chiefs, etc. However, surviving “duplicate” khipus with identical or closely matching numerical values – presumably counting the same item – sometimes have differently colored strings, which suggests a more regionally or thematically circumscribed code than can be gleaned from the chroniclers’ writings alone. At the same time, other portions of the chronicles have provided information that confirms modern decipherments: Leland Locke’s identification of three types of numerical khipu knots, for example, is consistent with the Inka Garcilaso de la Vega’s colonial-era description of tributary khipus as employing a decimal system of numeration. Despite the appeal of narratives found in the chronicles, more targeted, contextualized claims have emerged from documents that were never meant to be published: transcriptions of khipus – and documents mentioning khipus more broadly – that were produced during early 11 colonial legal and administrative events. Though they were never officially recognized as such, khipus were read aloud as probative evidence in the high courts by indigenous claimants seeking recompense for goods and services extorted from their communities in the first decades of the Spanish occupation. In such cases, a native cord reader would furnish one or more khipus, which informed oral testimony in Quechua or Aymara (both indigenous languages widely used in the Inka Empire and to this day in Andean countries) relating accounts from a period in question. An interpreter translated the testimony to Spanish, which was then entered into writing by a scribe present at the read-out. Some 10,000 lines of so- called “paper khipus” survive today in the General Archive of the Indies, in Seville, Spain. They remain one of the most distinctive products of the early-colonial encounter. This intrigue notwithstanding, can the study of khipu transcriptions produced following the Spanish conquest tell us anything about Inka khipus? In the first instance, it is worth noting that transcriptions were made of khipus produced both before and after the Spanish arrival. We thus have a baseline for making comparisons between the contents of both Inka and colonial examples, even if the corresponding khipus themselves have since been lost. What the transcriptions reveal is a general trend toward simple lists of items transferred to colonial overseers, as opposed to the more narratively complex accounts of Inka-era labor service. This would seem to imply that the diverse construction features of Inka khipus became progressively underutilized with the introduction of Spanish tribute to the Andes, though some scholars have argued that the difference simply reflects the substitution of one khipu genre for another. In either case, careful study of the transcriptions has shown that even those of colonial-era khipus contain valuable clues as to the structure and use of pre-Hispanic specimens. In 1975, anthropologist John V. Murra discovered that the categories of information in a 1560s khipu 12 transcription appeared in a consistent, repeating order. He hypothesized that these reflected the “ethnocategories” of the area’s khipu accounting, in which entries were listed in order of decreasing value. In this example, men and women were listed first, followed by camelids, textiles, grains (including maize and quinoa), and potatoes. Toward the end of the read-out – and thus valued comparatively less, according to Murra – were non-cultivated plant items (including wood and grasses), salt, and fish. It is likely that ordered categories were also in use in pre-Hispanic accounting khipus, though their exact sequence may well have differed across locales. As for the act of khipu reading, the clearest eyewitness accounts describe it as an active, vocal process, often supported by real-time calculation with yupanas. New research on paper khipus has gone further, identifying potential traces of the khipu reading process itself deposited in scribal corrections in the documents. Crossed-out phrases and marginal notations are consistent with answers to clarifying questions by cord readers; some numbers appear to have been repeated before being crossed out, as if the khipukamayuq had accidentally begun to read the previous pendant cord instead of its neighbor. Other numbers were reported without their associated labels, suggesting a type of “shorthand” khipu-reading style in which the repeating sequence of categories allowed for the omission of some names without loss of information or context. Nonetheless, preservation bias cannot be ignored. The surviving khipu transcriptions represent only the subset of khipus that were read out for colonial observers and recorded in written documentation. Cord keepers may have omitted secret or otherwise non-relevant portions of the khipus during their readings, resulting in a selective record of their true contents. And most known transcriptions pertain to numerical registers of tribute and census data – the other khipu genres described by the chroniclers are not well-represented, which could lead one to argue that such genres never actually existed. However, the overrepresentation of numerical information in the paper khipus aligns reasonably well with 13 the surviving corpus of physical specimens, which mostly exhibits knots consistent with the code defined by Leland Locke. This raises the ever-elusive prospect of finding a match, however defined, between a transcription and one or more specimens – what has been popularly dubbed a “Rosetta khipu,” alluding to the 19th century decipherment of Egyptian hieroglyphs. Khipu Decipherments, “Narrative” and Numerical Though an undisputed “Rosetta” match has yet to come out of sustained searches, these efforts represent only a small subset of current approaches to furthering khipu decipherment. One object of such studies – the enigmatic, so-called “narrative” khipu – merits immediate mention. From at least the 20th century, students of the khipu confronted a perplexing reality: if there were indeed nonnumerical khipus for history, laws, and genealogy, as the chroniclers suggest, then why don’t any appear to have survived? Why do the vast majority of extant khipus have knots that can be interpreted according to Locke’s numerical schema? Non- canonical khipus – that is, those with seemingly random knots – eventually became the default candidate for these nonnumerical, “narrative” specimens, and would informally be referred to as such in publications and academic presentations. Today, multiple researchers have called for caution on this point, describing the supposed distinction between “narrative” and numerical khipus as a modern scholarly invention. All numerical khipus contain narrative elements, insofar as their colors would have designated the names of items or categories. And even khipus with nonstandard strings – like those with multiple long knots in close succession, for example – often have dozens, if not hundreds of other strings that can be plainly interpreted according to the decimal code (Figure 6). Greater precision in terminology is warranted. 14 == Figure 6: Multiple Long Knots on Two Non-canonical Khipu Cords (Circled). Most of the Strings on this Khipu Otherwise Largely Conform to the Base-10 System == Of similar ambition, though of widely varying quality, have been studies that attempt to correlate spoken language with aspects of the khipu. Early attempts by researchers to find a khipu “alphabet” have largely been discredited as rife with unfounded assumptions and spurious correlations. However, recent research, informed by ethnography and colonial documents, has produced more careful hypotheses. Residents of San Juan de Collata, a highland village in Huarochirí Province (headwater region of the site of Pachacamac in the central highlands of Peru) reported to one anthropologist that a pair of colorful, knotless khipus conserved by their community are secret missives exchanged during colonial-era wars on behalf of the Inka. Several strings on each khipu have been correlated with syllabic pronunciations of two ayllus, or land-owning descent groups, involved in one anti-colonial rebellion in the area. However, further confirmation of this hypothesis – and others like it – has proven difficult, in part because the available evidence can fit multiple interpretations. The approach remains an ambitious and valuable one, nonetheless. The issues of correlation and sample size raise important questions for khipu decipherment. For example, recent research has reaffirmed the importance of kaytes – needlework bundles sometimes attached to the end of a khipu’s primary cord. These have been interpreted as subject markers that define the khipu’s contents for the reader. Indeed, kaytes appear in a 15 variety of shapes and designs, suggesting a rich inventory of signs for different khipu genres. However, a survey of some 650 catalogued khipus reveals that only 16 have kaytes. How, then, did the hundreds of khipus without kaytes indicate their subject matter? Some researchers have suggested that subtle distinctions in the primary cord may have served an analogous role in other khipus. In any case, the move to aggregate – to assess the representativeness of hypotheses derived from individual specimens – has provided an additional means of confirmation in khipu decipherment work. To this end, a combined, qualitative-quantitative approach has enabled the recent decipherment of two types of color patterning on Inka-style khipus. Through ethnographic and historical research, as well as an examination of surviving specimens, Sabine Hyland uncovered how labor accounting data were recorded and aggregated in the early-mid 20th century in Anchucaya, a central Andean community. Color-banded khipus, which are made up of groups of same-colored cords (e.g., colors 111, 222, 333 in a repeating sequence), recorded labor contributions at the ayllu level. These records were summarized at the village level using seriated khipus, which are composed of repeating sequences of colored strings (e.g., colors 123, 123, 123). In a subsequent quantitative analysis, Jon Clindaniel demonstrated that this basic distinction in color patterning is widespread and statistically significant for hundreds of ancient khipus as well, corroborating Hyland’s theory. It also reinforces the idea that there are meaningful continuities between Inka khipus and their modern counterparts, warranting further ethnographic research in this area. Aggregation even permits a return to the most mundane of khipu elements: its numerical knots. In the 1970s and 1980s, a mathematician (Marcia Ascher) and an anthropologist (Robert Ascher) carried out an extensive project to study khipus in museums and private collections on three continents. Of the more than 230 khipus that they were able to record, the 16 Aschers annotated many with complex mathematical relationships that they had identified between the strings. For example, in some khipus, adding the values on the first string in each cord group produces a sum that is recorded elsewhere on the same khipu. In others, dividing certain strings by others yields a consistent ratio. However, the Aschers only presented these formulae for individual khipus; they never assessed their representativeness across the global corpus of specimens. In new co-authored research, Ashok Khosla and I have done just that. Grouping the Ascher relationships into nine classes, we have found that the equations generalize unexpectedly well, characterizing some 75% of Inka-style khipus. A range of data science tools and methods revealed that “top cords” – the upward-oriented strings tied opposite to pendant cords – were a distinguishing characteristic of low-level accounting khipus used in everyday “working” settings. We have discovered that white-colored strings often served as markers for sums and groups of adjacent sums. And our ability to test millions of potential pendant cord combinations has allowed us, for the first time, to reunite two fragments of a broken khipu based purely on their mathematical interrelationships. In this way, our findings can contribute directly to khipu typology: the goal of grouping specimens in collections by genre and function. Aggregation and quantitative analysis provide discrete metrics – number of mathematical relations, density of equations, etc. – that can be used to distinguish between khipus in ways that are not immediately visible. And they might help to fill the inherent gaps in other approaches to khipu typology – as with kaytes, for example, which appear on only 2% of specimens – while explaining observed variation at the level of individual examples. Our ability to employ these methodologies relies, first and foremost, on the ongoing cataloguing and digitization of Inka khipus, which forms a final area of activity among those invested in decipherment. Beginning with the work of Leland Locke a century ago, researchers have often worked to produce comprehensive inventories of khipus in museums 17 and private collections. The Aschers enthusiastically continued this work as part of their mathematical-anthropological investigations. The newest inventory, which I prepared for a 2021 book, locates 1,386 khipus and khipu fragments in 143 collections in over 20 countries (Figure 7). They are conserved in museums of anthropology, history, art, computer history, libraries, and more. == Figure 7: Khipus in Museums and Private Collections == Once a khipu is identified, a researcher will often travel to document it. This is a time- intensive process that involves taking careful notes and measurements of everything from cord color to the length and number of knots on each string. These are recorded using a standardized notation format that allows for consistency across specimens. Photographs are taken to preserve a snapshot of the khipu before the further fading of its colors. With a written summary of the khipu, each data field can then be digitized and entered into a khipu database. The largest such project is the Open Khipu Repository, which contains 630 18 specimens as of the end of 2022. Its independent advisory board consists of Carrie Brezine, Jon Clindaniel, Ivan Ghezzi, Sabine Hyland, and me. The second largest khipu database is stored at the Museo Nacional de Arqueología, Antropología e Historia del Perú. In total, some 866 distinct khipu records – or about 60% of the known global inventory – are available in this format (Figure 8). A handful of additional khipu recordings are scattered across journal articles, books, and unpublished works. == Figure 8: Khipu Cataloguing and Digitization, 1920–2020 == Together, the cataloguing and digitization of Inka-style khipus supports conservation, diffusion, and decipherment. The records produce a permanent, online version of each specimen, with the data available for download by interested users. Computer programs can use the measurements to draw schematic diagrams of any specimen, helping to view color and structure in a standardized way (Figure 9). And the thousands of cord and knot observations in khipu databases allow for quantitative testing at multiple scales, both to evaluate hypotheses and to propose new ones. The American archaeologist Michael Coe once described large databases as one of the “fundamental pillars on which all successful decipherments have rested.” 19  == Figure 9: Diagram of Khipu VA42554, Ethnologisches Museum, Berlin == Looking Forward Where, then, does this leave the study of Inka khipus? What remains to be found? Some paths require continued commitment. Searches in the Archivo General de Indias and other archival collections will reveal new documents concerning the history of the khipu, including unexamined transcriptions of specimens read aloud for colonial observers. Dedicated engagement with museum institutions will enable the identification, cataloguing, and digitization of previously unknown specimens in global collections. Research with modern communities should also proceed to search for possible ethnographic analogies. Together, these will continue to grow the evidentiary base available to those studying the khipu. How we ought to analyze the evidence is, of course, an open question, though a few particularly promising routes and topics are becoming clearer to scholars. First, researchers interested in decipherment will need to consider the potential contributions of untapped quantitative methods, including, but not limited to, a suite of tools under the banner of artificial intelligence (AI). Machine learning, an application of AI that underlies everyday classification tools like e-mail spam filtering, merits further exploration. Trained on a series 20 of khipus with known or suspected genres (accounting, demographic, etc.), and given a list of physical khipu features, a machine learning algorithm can produce hypothetical groupings of “similar” khipus that can then be manually evaluated. Such applications can be coordinated with large-scale mathematical studies to produce working typologies of surviving specimens. These can then be correlated with information on archaeological find spot to produce targeted hypotheses regarding form and function. In parallel, those focusing their efforts on individual specimens may find value in revisiting the interpretations of earlier researchers. An especially important case concerns calendars and astronomical numbers, which have been a long-time favorite of scholars to identify in Inka khipus. In the 1920s, a Swedish scholar pointed to the apparent repetition of the number “7” in a sample of khipus in arguing that these served a dual function as puzzles for spirits and registers of celestial orbits. The theory would take hold for decades, before being dismissed by the Aschers as far-fetched and contrived. But more serious astronomical interpretations have since been raised, including one that identifies a khipu from a funerary context in Chachapoyas (northeastern Peru) as a late Inka-era biennial calendar and census of tributaries. Several chroniclers write that khipus recorded calendrical information, providing further support for research in this domain. The question that remains, however, is one that researchers more broadly will need to face in the coming years: how well must the data “fit” in order to declare a khipu deciphered? How should researchers treat contradictory evidence? When considering a particular interpretation, which components of the khipu are considered and which are ignored? An earnest answer to the last question becomes especially important in light of the high level of redundancy in Inka khipus. For example, I have studied specimens in museums in which differently colored groupings of cords are also separated from each other by gaps along the 21 khipu’s primary cord. Why use colors to distinguish strings that are already spatially separated into groups? In these cases, are the colors mere visual embellishment? Or do the colors and cord groupings happen to agree, but fulfill entirely different functions? Scholars must be weary of potential coincidences to avoid mistaking one khipu feature for another. A final area of emphasis is the study of khipus using scientific and experimental methods. Best known among these is radiocarbon dating, in which a small sample of cordage is taken, and its relative proportions of carbon isotopes measured. These enable an estimate of the khipu’s age, or at least of when the material used to make it was harvested. Several dozen khipu radiocarbon dates have previously been obtained, though these have often been for specimens on which little if any other research has been conducted. They are thus too decontextualized. More intentional radiocarbon dating should proceed with specific hypotheses in mind – for example, whether khipus said to pertain to a particular historical event indeed date to the correct period. Less developed at present are microscopy and dye analysis, which employ visual and chemical techniques. High-powered microscopes allow researchers to determine the structure of individual strings, revealing anomalous threads and fiber characteristics invisible to the naked eye. Dye analyses can suggest the ingredients of natural colorants, helping scholars to reconstruct khipus’ original colors, before the inevitable fading produced by exposure to light, heat, and human remains. These methods promise to introduce to khipu research tools already well established in the study of other archaeological material. As with any new endeavor, laboratory-based approaches will also contribute to decipherment in unforeseen ways. Almost exactly a century since Leland Locke’s decipherment of numerical knots, research on the Inka khipu remains as active as it is diverse. New evidence continues to surface, while new analyses of “old” data manage to produce surprising and unexpected interpretations. 22 Together, such initiatives have increasingly allowed us to describe khipus with some of the same terms with which colonial observers originally identified them – intricate; multicolored; even “historical.” Progress in decipherment remains gradual. However, our knowledge of the Inka khipu has unquestionably expanded. In the process, we inch ever closer to reading, in a meaningful way, the primary sources of Tawantinsuyu. Figure Captions Figure 1: Inka-style Khipu Fragments in the Museum der Kulturen, Basel, Switzerland. Photo by Manuel Medrano. Figure 2: Structure of an Inka-style Khipu. Figure 3: Numerical Khipu Knots. Drawing by Clarissa N. Pacyna. Figure 4: Solid, Mottled, Barber-Pole, and Color-Change Pendant Cords in an Inka-style Khipu. Photo by Manuel Medrano. Figure 5: Khipu “Traditions.” Figure 6: Multiple Long Knots on Two Non-canonical Khipu Cords (Circled). The Other Strings on this Khipu Otherwise Largely Conform to the Base-10 System. Photo by Manuel Medrano. Figure 7: Khipus in Museums and Private Collections. Figure 8: Khipu Cataloguing and Digitization, 1920–2020. Figure 9: Diagram of Khipu VA42554, Ethnologisches Museum, Berlin. Diagram by Ashok Khosla. 23 Recommended Readings Ascher, Marcia, and Robert Ascher. 1981. Mathematics of the Incas: Code of the Quipu. Ann Arbor: University of Michigan Press. Brokaw, Galen. 2010. A History of the Khipu. Cambridge: Cambridge University Press. Locke, L. Leland. 1923. The Ancient Quipu or Peruvian Knot Record. New York: American Museum of Natural History. Medrano, Manuel, and Galen Brokaw. 2023. “Quipu.” In Oxford Bibliographies in Latin American Studies, edited by Ben Vinson. New York: Oxford University Press. OKR Team. 2022. The Open Khipu Repository (v.2.0.0). Zenodo. https://doi.org/10.5281/zenodo.6908343. Biography Manuel Medrano is a PhD student in Latin American History at Harvard University, where he researches the history of antiquarianism, archaeology, and museums, with a focus on the material culture of the Andes. He holds degrees in Applied Mathematics (BA, Harvard) and Social Anthropology (MPhil, University of St Andrews), and is the author of Quipus: Mil años de historia anudada en los Andes y su futuro digital (Planeta, 2021), a new book on the state of khipu research. 24