Khipu Archives: Duplicate Accounts and Identity Labels in the Inka Knotted String Records
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Citation Urton, Gary. 2005. “Khipu Archives: Duplicate Accounts and Identity Labels in the Inka Knotted String Records.” Latin American Antiquity 16 (02) (June): 147–167. doi:10.2307/30042809.
Published Version doi:10.2307/30042809
Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:33702053
Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA KHIPU ARCHIVES: DUPLICATE ACCOUNTS AND IDENTITY LABELS IN THE INKA KNOTTED STRING RECORDS
Gary Urton
Accountsfrom the Spanish chronicles regardingInka record-keepingpractices by means of the knottedstring devices called khipu ("knot") indicate that these accounts were compiled in a system of "checks and balances." Each communityin the empire had a minimumoffour khipu accountants, all of whom are said by the chronicler Garcilaso de la Vegato have kept the same records. This study examines several examples of matching khipu accounts identified among sets of two or three khipu. The identification of matchingkhipu accounts has beenfacilitated by the recent developmentof a khipu database at Harvard University.It is argued that certain three-termnumerical sequences recorded in one set of three matching khipu from Chachapoyas, northern Peru, represent a type of numerical signifier that may have served as identity labels of the informationrecorded in this set of khipu. The long-range objective of this research is to investigate the informationrecorded on khipufrom various provenience zones around theformer Inka Empire that may representthe remains of khipu archives.
Relatos en las cronicas espaiiolas relativas a la prdicticaInka de mantenimientode registrospor medio de dispositivos de cordeles anudados denominadoskhipu ("nudo") indican que estos eran recopiladosdentro de un sistema de "controlesy ba- lances." Cada comunidaden el imperioposeia un minimode cuatro "contadores"o registradoresde khipu,todos los cuales, segin relata cronista Garcilaso de la Vega,llevaban y mantenianlos mismos registros.Este estudio examinadiversos ejemp- los afines y de concordanciacompartida, identificados entre conjuntosde dos o tres ejemplaresde khipu.La identificacidnde registrosde khipucon afinidady concordanciaha sido considerablementefacilitadapor el recientedesarrollo de una base de datos en la Universidadde Harvard.Se plantea que ciertas secuencias numdricasde tres elementos registradasen un con- junto de tres khipus afines de Chachapoyasen el norte del Peru',representan un tipo de significadornumerico que podrian haberfungido o desempentadocomo r6tulos de identidadde la informacidnregistrada en este conjuntode khipus.El objetivo a largo plazo de esta investigaciones la de averiguar la informacidnregistrada en ejemplaresde khipude diversas zonas del antiguo ImperioInka, que pudiesen representarlos remanentesde archivos de khipu.
neintriguing claim made by the chronicler village andfor each sortof calculation,so as of Inka life, Garcilasode la Vega, regard- to avoidfaults that might occur if therewere O ing Inkarecord keeping is thatthe knotted- few,saying that if therewere a numberof them, stringdevices known as khipu("knot") were used they would either all be at fault or none of in a system of checks andbalances. This systemis them [1966 (1609):331;my emphasis]. explainedby Garcilasoas follows: How are we to understandthe meaningof Gar- Although the quipucamayus [khipu- cilaso's claim? For instance, does his statement makers/keepers]were as accurateand honest mean that the four to 30 (or more) khipukeepers as we have said, theirnumber in each village in a given village kept exactly the same records, was in proportionto its population,and how- using the same recording principles and proce- eversmall, it hadat leastfour and so upwards dures?Who would have collated, compared,and to twenty or thirty. They all kept the same (if necessary)corrected the variousaccounts? Was records,and although one accountant or scribe all the informationrecorded on each of thesekhipu wasall thatwould have been necessary to keep duplicatedexactly andcompletely on otherkhipu, them,the Incas preferred to haveplenty in each or mightany two relatedkhipu have contained only
Gary Urton N Departmentof Anthropology,Peabody Museum 58B, 11 Divinity Avenue, HarvardUniversity, Cambridge, MA 02138-2019 ([email protected]).
Latin AmericanAntiquity, 16(2), 2005, pp. 147-167 Copyright@2005 by the Society for AmericanArchaeology
147 148 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005 partialor perhaps overlapping accounts? If we were analysis, I will reflect on how this materialmay to identify what we thoughtwere matchingkhipu relate to what Garcilasohad to say in the account accounts,how could we be certainthat this resulted cited earlierconcerning the multiplicityof record from two differentindividuals recording the same keepersin Inkaadministration and what these prac- informationas opposedto one khipukeeper copy- tices suggestabout the controland manipulation of ing his own account,or even a studentcopying an informationin the empire. accountof a more experiencedrecord keeper? I should clarifythat when I discuss "matching These arejust a few of the manyquestions that khipu,"I amreferring primarily to correspondences arisefrom a considerationof Garcilaso'sstatements in the numericalinformation encoded (i.e., knot- aboutInka record-keeping practices. While students ted) into the cordsof two or threedifferent khipu. of thekhipu have long been awareof thechecks and As has been understoodsince the earlyyears of the balances aspect of Inka khipu recordkeeping, no last century (Locke 1923), the majorityof Inka one to date has paid much attentionto this critical khipu have knots tied into their stringsin hierar- administrativepractice. I will addressthis lacunain chicaltiers that represent increasingly higher pow- khipu studies by consideringseveral examples of ers in the Inka decimal system of accounting khipuaccounts that seem to containif not the same, (Ascher and Ascher 1997; Urton 1997, 2003). In thenvery similardata, and that may, therefore, rep- additionto such knot-basedindicators of numeri- resent surviving examples of the administrative cal values,however, there are severalother means apparatusand practicesattested to in Garcilaso's wherebythe khipu keepers recorded other, or mod- statement.In the courseof this study,we may also ifying, types of information.These additionalsign be ablefor the firsttime to say somethingfairly con- featuresinclude color (bothof camelidhair and of crete about the use of "identitylabels" in khipu differentlycolored cotton), as well as severalforms accounts.We will encountersuch constructionsin of variationand patterningof khipu construction a set of threeduplicate, or matching,khipu samples features, such as material (primarilycamelid or from Chachapoyas,northern Peru. cotton)differences and directional variation in spin- My interestin pursuingthe topic of checks and ning, plying, knotting,and attachingkhipu cords balancesin the Inkakhipu arose from a rathersur- (see Conklin2002; Urton 1994, 2003). We do not prising developmentin a projectthat I am direct- yet understandwhat specific meanings might have ing at Harvard University, which is aimed at been attachedto any one of these latterelements, creatinga searchablekhipu database.' This project, nor of how they might, singly or in combination, which is underthe day-to-daydirection of Carrie have signedmeanings or values in the khipuinfor- Brezine (a mathematician,weaver, and database mation system.3Therefore, although I will occa- manager),is aimedat producing a databasethat can sionally discuss color similaritiesand differences, be queriedfor patternsamong numerous different my primary-and certainlyinitial-focus herewill khipufeatures, such as numbers,colors, anddirec- be on the examination of numerical matches tional variationsin the spin, ply, attachment,and between khipusamples. knotting of strings.A query of some of the first The largerobjective of this studyis to articulate khiputhat were entered into the database-22 sam- andbegin to developan explicitly archival approach ples discoveredat the Lake of the Condorssite, in to the study of the Inkakhipu. Such an approach, Chachapoyas, northern Peru-revealed an whichwas first(to my knowledge)proposed by the extremelyinteresting match of primarilynumeri- greatItalian-Peruvian student of the khipu,Carlos cal informationamong three different khipu. I will Radicatidi Primeglio(1949-50; see Urton2005),4 laterpresent the details of this match.At the time wouldfocus attentionon bringingtogether for com- of our discovery of khipu matches from Lake of parative analysis samples with common prove- the Condors,I was unawareof otherexamples of nance, or ones that actuallyderive from the same this phenomenonin the khipucorpus. However, I archaeological context. The value of such an subsequentlybecame awareof several additional approachwill be that it will (a) encouragecross- matches,and my objectivehere is to describeand collection study of samples with common prove- analyze the examples that are known to me at the nancein museumsaround the world,(b) encourage presenttime.2 On the basis of these dataand their the collection of informationfrom all khipu (pro- Urton] KHIPUARCHIVES 149 vided they are not too fragilefor study)regardless subsidiary,valued "4" on AS 194 (this value could of theirincomplete or fragmentarynature, and (c) have been registeredon the now broken second providethe comparativedata essential to investi- subsidiaryof Pl), and severaldifferences in string gating, in an informedand critical manner,Inka colorsbetween the two khipu.This instance appears record keeping and administrativeprocedures at to be a fairly straightforwardcase of a body of local,regional, and state levels of organization.I will informationrecorded on one khiputhat is repeated returnto the general question of developing an on another.The fact that the color values associ- archive-basedprogram of khipustudies in the con- atedwith the seriesof numberson these two khipu clusions.We begin our studyof khipuchecks and arenot identicalmight indicate that the khipu keep- balancesby looking at severalexamples of pairsof ers who constructedthe two recordshad their indi- matchingkhipu, all of which are from sites along vidual color sign values for indicating some the centraland southcoast of Peru. feature(s)of the identityof the numbersof objects, activities,etc., registeredon theirkhipu. Before too far the line Pairs of Matching Khipu going along interpretive for explainingcolor differencessuggested above, Whatappears to be a straightforwardexample of a however,we shouldrecognize that these two sam- correlationof informationregistered on two dif- ples might, in fact, have been constructedby the ferentkhipu occurs in the collection of the Amer- same person at two differenttimes, or perhapsin ican Museumof NaturalHistory (AMNH) in New relation to two different bodies of information. York.The provenanceof these khipu was said to Accordingto this alternativeexplanation, the same be nearCallango, in the Ica Valley.The two sam- numbersand groupings of individuals(= the num- ples in question, both made of cotton, bear the bers recordedon the pendantstrings) were identi- museumnumbers 41.2/6702 and41.2/6703. These fied in relationto differentcharacteristics (= the khipuhave been partiallydescribed, in tabularfor- stringcolors). Given the present state of knowledge mat,in Marciaand RobertAschers's (1978) Code of Inkarecord keeping by meansof the khipu,we of the Quipu: Databook.5In the Aschers's nota- cannot say what the precise meaningof the color tional system, these two khipu are identified, differences-or even the numericalsimilarities- respectively,as AS 194 andAS 195.6Iwill use these in these two sampleswas. Nonetheless,it seems a latterdesignations in the following discussion. reasonable assumption that this first pair of KhipuAS 194 bearstwo pendantstrings, the first "matched"khipu representsan expressionof the of which (P1) bearsthree subsidiaries. The firstof system of checks and balancesas describedin the the three subsidiaries(Plsl) itself bears two sub- previously cited testimony from Garcilasode la sidiaries (Plslsl/s2). The second pendantstring Vega. (P2) of KhipuAS 194, whichis a blank(i.e., it does The second example of matching khipu not carryany knots), is separatedfrom PI by 21 accounts comes from a pair of cotton khipu cm. The color7and numbervalues of the pendants included in a group of eight samples acquiredby and subsidiarieson AS 194 areshown in Figurela. the Museumfiir Vilkerkunde, in Berlin, in 1904. The other sample in this pair, Khipu AS 195, The provenanceof this set of eight khipuis given containsonly one pendantstring (P1). However,P1 in museumrecords as between Ica and Pisco, on bears three subsidiaries,the first of which (Plsl) the south coast of Peru.8The museum identifica- itself bears three subsidiaries(Plslsl/s2/s3). The tions andinvestigator numbers for the two samples thirdsubsidiary of P1 (= P1s3) is brokenoff from are VA16138A (=AS159) and VA16145A the pendantcord at 4 cm. The colors and numeri- (=AS 173). cal values assigned by the Aschers to the strings KhipuAS159 is composedof a total of 35 pen- composingAS 195 are given in Figure lb. dant strings.The first seven pendantstrings (with As we see in Figures la and b, the numerical any subsidiaries)are diagrammedin a schematic valuesof knots on the pendantsand subsidiariesof fashionin Figure2a. AS 173 is composedof a total AS 194 and 195 are almostidentical. (All knots on of only 13 pendantstrings. In Figure2b, I provide thesetwo khipuare tied as Z-knots).The majordif- a schematic diagram of the first eight pendant ferences are in the absence of a thirdpendant, or stringsand subsidiariesof this sample. 150 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005
2 1 1
62(W) 62(B) 4(B) 4(B) 4(KG:W) ?(LB) 4(B:KG) 4(B-W) ' 8(B) 8(B) 3 ?(LB) (B)
120(W) 120(B)
(a)-AS194 (b)-AS195
Figure 1. Khipu matching pair: AS194 and AS195.7
The seven pendantstrings (P1-7) on AS 159 are provenancebetween Ica and Pisco, while AS 123 identical in terms of their numericalvalues and bearsa provenanceof Ica. These two samplesare their pendant/subsidiarystructure to seven pen- of notablydifferent sizes: AS 114 is composed of dant strings(P2-8) on AS 173. The remainingfive 339 pendantstrings whereas AS 123 bearsonly 70 pendantstrings (P9-13) of AS 173 do not contain strings. Both samples have numeroussubsidiary matches with any segment of the remaining 28 cords on theirpendants, although no subsidiaries pendants(P8-35) on AS 159. Thus, it is as though are present within the two stretches of pendant the firstone-fifth (i.e., P1-7) of AS 159 is replicated stringsexamined here. The values of knots regis- on the majority of AS 173. Said another way, tered on the two segments of pendantcords are AS 173 might have been the source of the infor- shown in Figure3. mationrecorded in the firstpart of AS 159. In this Althoughof very differentsizes, the matching scenario,however, the remainingfour-fifths of the series of 10 pendantcords on these two samples datain AS 159 is unaccountedfor, at least withpre- are found at virtuallythe same locations on their sent information. This raises the question of respectivekhipu; that is, the set of 10 matching whetheror not theremight be otherkhipu with Ica- stringson AS 114is foundon pendants40-49, while Pisco provenancethat recorded other segments of the 10 stringson AS 123 are located on pendants pendantson AS 159, andeven the remainingshort, 41-50. Thus,there are 39 stringspreceding and 290 unmatchedsegment of AS173. We have not yet stringsfollowing the segment from AS 114 under succeeded in identifying such samples from the discussion,and there are 40 stringspreceding and datain our database. 20 strings following the segment shown from The next exampleof matchingkhipu is another AS123. This raises the question: How do the pairfrom the Museumfuir V6lkerkunde in Berlin; remainderof thependant values on thesetwo khipu these are samplesVA16148 andVA47085, which relateto eachother? From a carefulcomparison (see bear(respectively) the Ascher investigator numbers the Ascher tables for AS114 and AS 123 at AS 114 andAS 123. This matchingpair was iden- http://instructl.cit.comell.edu/research/quipu- tifiedin a searchof the khipuentered into the Har- ascher/),we findno additionalsegments that match vard Khipu Database. Khipu AS114 has a (numerically)between these two khipu. Urton] KHIPUARCHIVES 151
cord # 1 isl 2 3 4 5 6 7 ,.,35
knot values: 1 18+2 16+1 16 16 18 12 16 color: (W) (W) (B:W)(B:W) (B:W) (B:W) (B) (B:W)
cord # 1 2 2s1 3 4 5 6 7 8 ...13
KnOT values: 1 1 18+2 16+1 16 16 18 12 16 color: (B:W) (W) (W) (B) (B) (B) (B) (B) (B)
Figure 2. Khipu matching pair: a. AS159 (above) and b. AS173 (below).7
The main similaritiesbetween the two account- respectivehost khipu.This implies thatthe match- ing contexts in which the numberseries defined ing segmentsmay representinformation that came above are located are that:(a) thereis at least one from a commonsource. For example, these match- null (i.e., zero valued)string before and aftereach ing numericaldata could have come fromtwo dif- of our matching segments; and (b) the pendant ferent khipu keepers who were responsible for stringson which the respective10-string segments recordinginformation on the same task or char- are located on the two samples are all the same acteristic(s)of a single accountinggroup, such as color,though the color differsslightly between the the kin-based groups known as ayllus (see two series-that is, the 10 stringsin AS 114 are all Salomon 2002). Alternatively,a section of one of coloredgrayish brown (HB), while those in AS 123 these khipu (e.g., AS 123) could have been the are all grayishyellowish brown(EB) source for the account recordedin the compara- My suppositionis thatthese matching10-string ble section on the other khipu (AS 114). The fact segments may represent"isolable" units within that the remainderof the datarecorded in the two their respective khipu, suggesting that these seg- accountsis differentsuggests thatthe khipukeep- ments could have been accountedfor apartfrom ers who retainedthese recordsshared only this one the informationon the neighboringstrings of their accountingresponsibility. 152 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005
pendant cord # ...40 41 42 43 44 45 46 47 48 49 50.. primarycord AS114 color: all HB value: 40 9 57 30 56 80 21 8 22 12
AS123 color: all EB value: 40 9 57 30 56 80 21 8 22 12
Figure 3. Khipu matching pair: AS114 and AS123.7
Close Matchesor SuccessiveAccountings? In analyzingthe information in Figure5, we see, first,that the color of pairedstrings in the two parts We turnnow to an exampleof matchingkhipu seg- of the khipuare in most cases identical.As for the ments that occurs within one of the samplesjust knotvalues on correspondingstrings in PartsA and discussed-Khipu AS114. Because AS114 con- B, these are identicalin some cases, close in oth- tains a total of 339 pendantstrings, it is impossi- ers, and quite far apartin severalcases. However, ble to representin a diagramevery string along with if one looks downthe lengthof pairedvalues in the theirnumerical and color values.Nonetheless, it is six segmentsof AS 114, PartsA and B, one will be importantfor gainingclarity on this complexkhipu struckboth by the similarityin the overallpairing to illustratein at least a schematicmanner the type of magnitudes and colors registered in the two of comparativeaccount keeping in this sample. halves of this khipu. The illustrationof selected stringsfrom AS 114 The questionthat confrontsus in viewing Fig- thatI will analyze(see Figure4) is arrivedat in the ure 5 is what can this particularpatterning have following manner:If we wereto fold KhipuAS 114 meantto the khipukeeper who was chargedwith into two equalparts, we wouldhave one partcom- keepingthis account in thetwo halvesof his khipu? posed of strings1-169 anda secondpart composed This seems clearlynot to have been an instanceof of strings 170-339. I will referto these half-khipu two differentkhipu keepers at work on separate, parts as (respectively)A and B. However,I must related accounts,as in the situationdescribed by enter a caveat before examining several sets of Garcilasocited earlier.Rather, this seems to be a pairedvalues in the two halves of KhipuAS114. recordof a single accountant'sdetailing, in the two Thereare severalsegments in the pairedhalves of halves of his khipu, two different but similar this khiputhat contain strings with no knots;thus, accountingstates or circumstances.For example, these strings contain no numericalvalues. I will KhipuAS 114 couldbe an accountadjustment, per- eliminatethe segmentsof null valuedstrings in our haps resultingfrom recordinginformation on the analysis(and their illustration). The locationsof the same topic at two differenttimes. The most direct eliminatedsections are indicated in Figure5 by hor- examplewould be drawnfrom a demographiccon- izontallines drawnacross the columnsof thepaired text. For instance,one half (e.g., PartA) of Khipu sets of strings.The locationand quantity of nullval- AS 114 mighthave been the census of the popula- ued stringswithin the six pairedsets can be deter- tion living in some given region aroundpresent- mined by looking at the breaks in the number day Ica at one pointin time andthe otherhalf (Part sequences in the columns labeled "cordnumber" B) could have been the recordof the census of that in the figure.These operationson AS 114 produce same populationmade at anothertime. 11 pairedgroups of strings.We will look specifi- Such a processof countingand recounting pop- cally at the firstsix sets. ulationsand recording the results in khipudescribed Urton] KHIPUARCHIVES 153
A) (B)
Figure4. The two-partorganization of KhipuAS114. above calls to mind the observationson tribute thatis, althoughthe numbersof people in the dif- accountingreadjustments made by CatherineJulien ferentgroups changed in the two differentaccount- (1988) in her seminal study,"How Inca Decimal ing periods,their identities as groupsor classes of AdministrationWorked." Such counts and recounts people remainedthe same. We will returnlater to of populationswere also commonpractices in the the question of identity labels in another set of colonialcensus procedures (for which records were matchingkhipu. kept both in written documents and in khipu) After this expanded analysis of AS114, we known as visitas and revisitas (see Guevara-Gil returnto the earlierdiscussion of thepair of match- and Salomon 1994). It is also instructiveto note ing khipuin Figure3. We saw in thatpair of sam- that, in the early cuneiform tablets from ples that 10-stringsegments on AS 114 andAS 123 Mesopotamia, similar "close matches" occur in containedmatching data. Having now examined the certainaccounting circumstances, for instance,in overall bilateral organization and recording of the debit and credit versionsof tabletspertaining numericalinformation in AS 114, we can focus on to the same transaction,as well as in successive the segmentof Figure5 in the farleft-hand column yearlyaccounts of such thingsas census or tribute labeledSection 2. We now see thatSection 2 in Part records(see Nissen et al. 1993:43).9In sum, I sug- A of AS114 (Figure 5) is the same segment of gest thatthe differencesin numericalvalues in Parts strings that was earlier compared with Khipu A and B in Figure 5 may have been the result of AS 123, in Figure3. I suggestthat what we may be the khipu keeper having recordeddifferent num- viewing in these two figures is an example of a bers of people (or some other variableresource) "sourcekhipu" for a segmentof a larger,summary- within a certaincommunity or region in or around type khipu. The 10-string segment from Khipu Ica at two differenttimes. The colors of stringsin AS123 shown in Figure 3 might represent the the varioussections of the two partsof this sample sourceof theinformation recorded in Section2, Part might have fulfilled identity-labelingfunctions; A of KhipuAS114, in Figure 5. Thus, we might 154 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005
A B
cordnumbertotalvalue subsidiarytotalvalue color cordnumber totalvalue subsidiarytotalvalue color 20
40 40 HB 200 40 HB 41 9 HB 201 10 HB 42 57 HB 202 53 HB 43 30 HB 203 30 HB 2 44 56 HB 204 74 HB 45 80 HB 205 75 HB 46 21 HB 206 22 HB 47 8 HB 207 22 HB 48 22 HB 208 23 HB 49 12 HB 209 21 HB
56 110 B 216 109 B: B 56sl 8 CB:B 216sl 5 CB:B 3 57 10 B 217 101 B 58 88 B 218 110 B 59 76 B 219 98 B: B
66 231 B 226 203 YB: B 67 240 B 227 212 YB: B 4 68 231 B 228 210 YB: B 69 152 B 229 213 YB
80 100 GO 240 100 GO 81 30 GO 241 43 GO 82 32 GO 242 41 GO 83 37 GO 243 33 GO 84 61 GO 244 60 GO 84sl1 10 CB 244sl1 10 CB 5 85
97 5 B 257 4 B 98 5 B 258 4 B 99 2 B 259 4 B 100
Figure 5. Knot values and colors in the first six paired sections of AS114.7 Urton] KHIPUARCHIVES 155
say thatKhipu AS 123 couldhave been the account site of Puruchuco,located in the Rimac Valley, of anayllu-level record keeper, part of whose infor- about 11.5 km northeastof Lima.This cache was mation was incorporatedin Section 2 of AS 114, inside an unslippedolla underthe floor of a small PartA. This would suggestthat AS 114 could have house built against the wall of a large "villa"at been composed from 11 different(ayllu-based?) Puruchuco(Mackey 1970:65-66). The three cot- khipu keepers' accounts, one for each section ton khipu are labeled No. 2, No. 3, and No. 9 in shown in Figure5. Mackey's numberingscheme and are composed Withthe aid of the khipudatabase under devel- (respectively)of 74, 71 and 62 pendantstrings. opmentat HarvardUniversity, we have been able Given the size and complexity of the three to identifyseveral other examples of reassessment, Puruchucokhipu, it is possible only to illustrate or readjustment,khipu accounts similar to thatseen summaryinformation recorded on them (see Fig- in AS 114. Anothersuch exampleis shown in Fig- ure 7a-c). In Figure7, we see the numbervalues ure 6a and b. Figure 6a shows the numericalval- andcolor designations'0 for pendant strings on sam- ues and colors of the 13 stringscomposing khipu ples No. 2 (Figure7a), No. 9 (Figure7b), and No. sample AS1 16, with Ica provenance, in the 3 (Figure7c). This informationwas initiallytaken Museum ffir V61kerkundein Berlin (VA 47125). from CarolMackey's (1970) study.However, Car- Figure6b shows the numbersand colors of strings rie Brezine and I recently undertooka complete on AS 150, a samplealso fromIca in the Berlincol- restudyof thesethree (and all otheravailable) khipu lection (VA 47109). It containsa total of 27 pen- in the Puruchucoarchive (Urton and Brezine 2005; dantstrings. see the data tables of the Puruchucoarchive at: In Figure6, we see thatthe numericalvalues on http://khipukamayuq.fas.harvard.edu/).The khipu thematching segments of thesetwo khipuare iden- labeled No. 9 by Mackey (Figure7b) was not in ticalor very close. However,the differences are reg- the PuruchucoMuseum at the time of our study (I ularin the sense that,when the pairedvalues differ, am unsureof thewhereabouts of this sample).Each the value on AS 116 is alwaysless thanits mate in set of columns in Figure 7 representsthe render- AS 150. Thus, like the two half-khipuaccounts in ing (respectively)of: the color designationnota- AS 114, the two samplesin Figure6 may countthe tions used by Mackey (e.g., Figure 7a = sameitems at two differenttimes; in thiscase, how- CGBC2BC...),and the numericalvalues of knots ever,the numbers of itemscounted will, in all cases, tied onto pendant strings (e.g., Figure 7a = have increasedover the time periodconcerned (if 1113821...) as readeither by Mackeyor by Urton KhipuAS 116 precededAS 150), or they will have and Brezine.A few of my own readingsof numer- decreased(if AS 150 precededAS 116). The colors ical valuesof knotson KhipuNo. 2 andNo. 3 (Fig. of the stringsin this pairare also quite similarand 7a andc) differedfrom those recordedby Mackey containthe same generalpatterning of the alterna- (1970)." Therefore,some of the values in Figure tion of a white (W) stringand a stringcolored either 7 have been changedfrom the values reportedby moderatereddish brown (RB), in AS 116, orbrown- Mackey. ish orange (SB), in AS150. Such consistency in What is immediatelyof interestis the striking color patterningmay indicatethat the two khipu similarity in numericalvalues registeredon the recordedthe same identities,or classes of objects. three khipu in Figure 7. As for the nonmatching numericalvalues on these three khipu, these are to the that obtain Three-Way Khipu Matches keyed particularrelationships between Figure 7a and 7c and the centralkhipu, We have looked at matchesin eithertwo khipuor 7b. Specifically,if a numbervalue does not match the two halves of a single sample. In this section, across all three samples, one or the other of two we will look at two significantlymore complex circumstancesis indicated in Figure 7. In those examplesof matches,each involvingthree khipu. cases in which Khipu No. 9 (Figure7b) shares a The firstis drawninitially from material presented particularnumerical value with KhipuNo. 2 (Fig- by CarolMackey's (1970) KnotRecords inAncient ure 7a), but where this value does not appearon and ModernPeru. The samples were includedin KhipuNo. 3 (Figure7c), an arrowpoints from that an archivecomposed of 21 khipudiscovered at the numberin Figure7a to the correspondingnumber 156 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005
Ica AS116 Ica ASl50
cordnumbertotalvalue color cordnumbertotalvalue subsidiarytotalvaluecolor 1 170 W 1 155 MB 2 64 SB 1s1 2 LB 3 84 W 2 151 W 4 37 AB 2s1 2 LB 5 81 W 3 117 RB 6 9 SB 4 475 W 7 52 W 5 182 W 8 2 SB 6 65 RB 9 26 W 7 87 W 10 2 AB 8 38 RB 11 27 AB 9 92 W 12 2 AB 10 10 RB 13
Figure 6. Khipu matching pair: a. AS116 and b. AS150.7 Urton] KHIPUARCHIVES 157
Figure 7. Three matching khipu from Puruchuco.7 158 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005 in Figure7b. This is intendedto suggest thatFig- keeper who retainedthe khipu in Figure 7b was ure 7a may have been the sourcefor that particu- charged with resolving differences between the lar numericalvalue in the Figure7b sample.And khipu keepers who constructed the accounts second, in a few cases, the khipu in Figure 7b recordedin the samples in Figures7a and 7c and (KhipuNo. 9) containsnumbers that are not found that he/she more commonly agreed with or in either KhipuNo. 2 or No. 3; in such instances, acceptedthe data providedby 7a than those pro- these numbersin Figure7b are shaded.This latter vided by 7c. notationis meantto indicatethat this value is unique A thirdobservation that would seem to support to khipu No. 9 (and perhapswas obtainedfrom the interpretationgiven aboveis thatthe colorcod- some othersource). It shouldalso be statedthat no ing used by the Figure7b khipukeeper was more values are sharedonly betweenKhipu No. 3 (Fig- similarto thatused by the makerof the khipuin 7a ure 7c) and Khipu No. 9 (Figure7b), and no val- thanit was to thatused by the makerof the khipu ues exist both in Figure7a and Figure7c that are in 7c. Specifically,the khipu in Figure 7b most not also found in Figure 7b. As a result of these commonly resortsto the color sequence: BAG2 observations,we can concludethat the khipu in Fig- (see Note 10 for translationof Mackeycolor nota- ures 7a and7b aremost alikeand that those in Fig- tions); the Figure 7a khipu also commonly uses ures 7a and 7c are least alike. BAG2, but with an occasionaladdition (at the top What do the above observationssuggest about of the column) of BCG2 (see Note 10); the khipu the relationshipsamong these three khipu from in Figure7c, on the otherhand, primarily displays Puruchuco?I contend, first, that the three khipu the color patterninglabeled BCG2 andcontains no depicted schematicallyin Figures 7a-c represent instanceof thecolor sequence BAG2. Thus, the Fig- differentversions of the same accountingcircum- ure7b khipumost commonly shares both its numer- stance. For example, these may be the khipu of ical valuesand its colordesignations with the khipu three differentkhipu keeperscharged with keep- in 7a, while also sharing much of its numerical ing the same account,as Garcilaso'sstatement at (thoughnot its color) informationwith thatin 7c. the beginningof this articlesuggests occurred quite In summary,I arguethat Figures 7a-c representa commonly in Inkarecord keeping. set of khiputhat were the productsof datacollec- It is importantto statethat the numericalvalues tion and accounting adjustments that went on on the three khipu in Figure 7 are, on the whole, amongeither two or threekhipu keepers who were close enough to each otherthat I do not think we charged,as Garcilasosuggests they always were, are confrontedhere with a more complex, three- with "keepingthe same account." khipu version of the kind of pairedaccounts dis- Our second example of a three-waygroup of cussed in the precedingsection. It was arguedthere matchingkhipu comes fromthe northernPeruvian thatthe differencesin thoseparticular paired khipu (Chachapoyas)site of Lakeof the Condors(Lerche (see especially Figures5 and 6) resultedfrom dif- 1999; von Hagen 2000; von Hagen and Guilldn ferentrecords produced in successiveaccountings. 1998). An archiveof 32 khipu was includedwith In the case of the threekhipu shown in Figure7, I the 220 mummy bundles and associated burial think that the values recordedare close enough goods foundin two rockoverhang sites aroundthe among themselves to supportthe suggestion that lake.Ten were too fragileand fragmentary to allow these are three differentversions drawnfrom the for examination.Thus, 22 khipufrom this site are same accountingepisode, or circumstance. available for study (see descriptions at http:// Second, I suggest that the accountsin Figures khipukamayuq.fas.harvard.edu/). 7a and 7b were more similar to each other than Because they were found with relativelygood those between either 7a and c or 7b and c either archaeologicalcontext, the Lake of the Condors because the khipu keepers who constructedthe khipuseemed to offergreat promise in allowingus khipu in 7a and 7b saw things more nearly alike to identify matchesof numericaland other types (and differentlyfrom the khipu keeper who con- of informationamong samples. During the first structedthe khipu in 7c) or because the khipu in week after we had begun queryingthe data from 7b was the "adjusted,"or "standardized,"account. the Chachapoya archive in our database, we The lattersuggestion would imply that the khipu encountered a quite remarkableset of matches Urton] KHIPUARCHIVES 159 amongthree of the samples:UR6, 9, and21.12Now, 1997;Espinoza S. 1967;Urton 2001). I wouldnote I have previouslypublished an extensive analysis thatthe populationthat lived in the immediatearea of one of these khipu-UR6 (Urton2001). In that of Lakeof the Condorsat the time of the conquest study,I arguedthat this largeand elaboratekhipu was composedof peoplebelonging to theChilchos representeda two-year calendarthat was used in ethnicgroup and that the Chilchoswere organized the organizationand accountingof tributelabor in into nine ayllu (Lerche 1995). Thus, Khipu UR6 centralChachapoyas in late prehispanicand pos- may representan accountof the laborservice per- sibly early colonial times. I will begin by briefly formed by the Chilcho mit'ayuq (state service reviewingthe featuresof this sample that led me workers)either over two differentyears, or in two to the calendricalhypothesis, as this will set the differentaccounting groups (one of approximately stage for the analysis of the matchesrecently dis- 1,000 and anotherof approximately2,000 work- coveredbetween KhipuUR6 and two other sam- ers) in a single year,during late prehispanictimes. ples. With this background,we turnto the matches KhipuUR6 is composedof a total of 762 pen- that were recentlyidentified between KhipuUR6 dant cords;730 of these cords are organizedinto andtwo othersfrom the archiveat Lake of theCon- 24 sets of strings,each set of which is made up of dors.Table 1 presentsthe author'srecord of numer- 29 to 31 pendantcords. The magnitudeand range ical values registeredin the knots tied into all the of the numbersof cords suggestedto me thatthey pendantcords of UR6. (Note:Pendant strings with might represent a frameworkof 24 month-like null value are eliminatedfrom the accountingin units.The 24 sets of cordsare composed of paired Table 1.) Table1 is dividedinto fourhalf-year seg- groupsof: (a) 20, 21, or 22 pendantcords thatare ments, labeled (a)-(d). The groups of numbers attacheddirectly to the primarycord; and (b) 8, 9, below the dottedline in Table 1 representthe knot or 10 pendantcords attached to the maincord indi- valueson pendantscords in thissection of thekhipu rectly,by means of what I refer to as "loop pen- that do not conformto the calendricalstructure of dants."Loop pendantsare composed of pendant UR6. cords attached to a string whose two ends are The segment of the calendarthat we will be attachedto the primarycord; thus, the string,with most directlyconcerned with here, as it contains its attachedpendant cords, hangs down (in a "loop") the informationmatching two other khipu, is an from the primarycord (see Urton 2001:136-138, approximatelyfour-month period that extends from Figures 5 and 7). I arguedthat the 730 pendant nearthe beginning of thethirteenth through the end stringsorganized into 24 month-likesets, each com- of the sixteenthmonths. This is the portionof Sec- posed of 29-31 pendantcords, provideda calen- tion (c)-the thirdsix-month period of thetwo-year dricalframework for accountingfor tributelabor calendar-that appearsin bold italicsin Table 1. (I overa periodof two twelve-monthsolar years (i.e., will explain below why several additionalsets of 2 x 365 = 730). The calendricalstructure of Khipu numbersinside and outside the italicized section UR6 is shown in schematic form in Figure 8. in Table 1 are underlined.) Groupsof pendantstrings that do not conformto The two khiputhat matchthe four-monthsec- the month-likeorganization of pendantstrings in tion of datain bold italics in Table2 are UR9 and KhipuUR6 are circled. UR21. Thesethree samples are brought together in I also documentedin my earlierstudy that the the threegroups of columns in Figure9. Each set numericalvalues of knotstied into the 730 pendant of columnsin Figure9 containsthe cordnumbers stringsthat compose thetwo-year calendar contain andtheir respective numerical values and color(s). a total count of 2,962.13I suggestedthat this knot In Figure 9, the left-handset of columns pertains counttotal represented an actualaccounting of the to KhipuUR9, the centralset of columnsis taken ideal organizationof tresguarangas (3,000 tribute from the four-month segment of UR6 defined payers)that were said, in Spanishdocuments pro- above, and the right-handset of columns pertains ducedin this regionduring the 1540s-70s, to have to UR21. The designation"LP_," which appears been enumeratedon a khiputhat was at thattime in the left handcolumn in the centralset of columns in the possession of a native Chachapoyakhipu (i.e., UR6), refersto "LoopPendants" (see above). keeper in the area named Guaman (Schjellerup The similaritiesbetween the numericalvalues 160 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005
Pendant/Loop Pendant Pairs (1) 20 9 (1) 21 9 21 (a) 9 =179 21 9 21 9 21 9 One =362 21 Year 9 21 10 22 9 (b) 22 =183 8 21 9 22 9 .730 + 2 . 365 21 9 22 9 22 9 (c) (4) =185 22 9 22 9 22 9 Two =368 22 Year 9 22 9 22 8 (d) 22 =183 9 22 8 21 9 4 2 5 2 5 Figure 8. The calendrical organization of pendant strings on Khipu UR6. Urton] KHIPUARCHIVES 161
Table 1. NumericalValues on Khipu UR6. UR 6 (a) 2, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 9, 2, 1, 2, 2, 4, 1, 2, 5, 1, 4,1, 15, 2, 1, 1, 7, 1, 7, 12, 30, 65, 20, 1, 1, 2, 1, 1, 15, 10, 1, 3, 1, 1, 4, 2, 1, 1, 2, 1, 12, 2, 15, 3, 3, 2, 4, 1, 1, 1, 4+3, 1, 1, 1+1, 3+3, 1, 1, 1, 1, 10, 2, 1, 11, 2, 7, 2, 7, 2, 8, 2, 1+1, 2, 1, 1+1, 3+2, 1, 1, 1, 1, 1, 6, 1, 2, 1, 1, 2+1, 4, 9, 2, 5, 2, 9, 2, 2, 18+2, 2, 4+2, 2, 16+4, 1, 10+3+6, 521, 10+8+6, 1, 1, 2, 2, 2, 7, 1, 1, 10, 3, 7, 3, 2, 2, 14, 2, 1, 7, 2, 1, 6, 1, 30, 80, 20, 1, 3, 2, 1, 3, 1, 1, 1, 10, 18, 2, 1, 1, 1, 1, 1,6, (b) 1, 1, 3, 1, 3, 1, 8, 6, 9, 8, 3, 1, 2, 1,2,4, 11,1, 1, 2, 6, 1, 1, 1, 13, 9, 7, 6, 2, 8, 2, 5, 1, 9, 1, 15, 40,2, 2, 2, 2, 2, 3, 3, 9, 3, 2, 1, 12, 1, 6, 1, 6, 9, 19, 2, 1, 9, 4, 4, 1, 1, 20, 71, 35, Table 2. IdentityLabels in KhipuUR6. 2, 2, 2, 3, 1, 1, 4, 1, 2, 1, 3, 1, 15, 21, 2, 5, 1, 1, 1, 5, 1, 5, (a) 2, 2, 1, 1, 3, 3, 1, 13, 1, 3, 4, 3, 10, 9, 10, 5, 30-65-20 2, 3, 5, 1, 30-80-20 2, 1, 2, 2, 1, 2, 10, 1, 7, 1, 1, 6, 10, 5, 15, 5, 7, 1, 5, 1, 5, 1, 12,3520, (b) (c) 15-40-22 2, 1, 1, 2, 2, 8, 1, 2, 9, 2, 5, 1, 2, 7, 14, 20-71-35 2, 1, 8, 4, 3, 1, 1, 20, 61, 20, 12-35-20 2,1, 3,2, 3, 1, 2, 1, 14, 16, 4, 2, 1, 1, 4, 1, 1, 5, (c) 1, 1, 2, 1, 1, 4, 7, 1, 2, 1, 1,3, 3, 11, 10, 3, 3, 20-61-20 2,1,3,1,5,1, 1, 1, 1, 1, 10, 9, 10-40-160 2, 2, 3, 2, 7, 1, 3, 1, 1, 1, 6, 11, 5, 7, 5, 10-40-16 6, 1, 5, 1, 5, 1, 1, 11, 35, 20 1, 1,, 1, 2, 2, 3, 2, 2, 2, 5, 4, 4, (d) 1, 4, 1, 1, 2, 1, 10, 40, 16, 10-30-10 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 5, 2, 5, 10-30-10 191, 1, 5, (d) 1, 1, 1, 3, 1, 1, 2, 3, 4, 4, 5, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 3, 1, 4, 8, 3, 3,3, 5, 1, 3, 1, 3, 1, 1030, 10, 1, 2, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 2, 4, 4, 1, 3, 1, 3, 1, 1, 1, 1,2,3, 1, 1, 2, 1, 1, 1,2,6,4,7, 5, 4, 1, 3+1, 1, 2, 10, 1, 30, 2, 10, 1, 1, 1, 1, 1, 2, 3, 3, 1, 3, 1, 2, 3, 20, 7,
1, 1, 1, 4,4, 2,2,2, 1, 1, 1, 1, 1, 1, 2+1 162 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005 registeredin the threekhipu shown in Figure9 are that these ancestralmummies, along with their striking.On the basis of these similarities,I argue khipu,may havebeen located elsewhere in the cen- that UR9 and UR21 may representdifferent ver- tral Chachapoyasregion. sions, drafts,or cross-references(in the Garcilas- It is relevantto note that accountingin four- can sense) of the information contained in the month periods,as in khipu samples UR9, UR21, four-monthsegment of UR6. How mightthis com- and a segmentof UR6, was apparentlya standard plex set of matchingnumerical values on threedif- featureof Inkarecord-keeping practices. Such an ferent khipu from the archive at Lake of the accountingperiodicity is suggested,for instance, Condorshave come about?Phrased another way, in the testimony of Polo de Ondegardo whatcan this exampleof matchingkhipu accounts (1916:146-147), who says thatin Inkatimes, peo- teach us about Inka record-keepingpractices, at ple deliveredtheir tribute to Cusco on threeocca- least in this far northernregion of the empire?I sions throughout the year; this suggests a 3 x believe thereare two featuresof this set of match- 4-month accounting periodicity (= 12 months). ing khiputhat we shouldfocus on in orderto arrive Juande Matienzonotes a similaraccounting peri- at an interpretationof the types of information odicity in early colonial times as follows: recordedon these three samples and the way the if anyIndian requests something or accusesa information registered on them may have been principalof something,he cannotdo so before compiled, compared,and synthesized. the 'alcaldes' but [he must do it] The firstfeature I stressis thatthe match between (mayors), beforethe Spanish 'Corregidor,' and, if he [the samplesUR9 and UR21 with UR6 involves about Corregidor] is not available, before the a sixth of the data (i.e., four out of 24 months) Tucuirico,so thathe [theTucuirico] puts it in recordedon whatI hypothesizedearlier was a trib- his quipofor the record, and every four months utary calendar-UR6. Building on this earlier he goes withthe quipo to the Corregidorin the hypothesis,I now suggestthat UR9 andUR21 rep- city, so that he [the latter]expediently does resentaccounts of ayllu laborersthat were retained justice about the complaints that he [the by two khipu keepers who were responsiblefor Tucuirico]brings by the quipo,without hav- recordinginformation pertaining to one or more ing to receivethose who madethe complaints aylluswhose serviceduty (or duties) fell duringthe when these are small things [Matienzo four-monthperiod in question.The two ayllu-level 1967:55; translatedby R. T. Zuidema;my khipu keepers who retained samples UR9 and emphasis]. UR21 would have reportedthe contents of their respectivekhipu to a third,probably higher level, Thus,the factthat UR9 andUR21 containsome khipukeeper. The latterofficial-i.e., the khipuka- mannerof accountingduring what appearsto be a mayuq who retainedUR6-would have had the four-monthsegment of UR6 accordswell withwhat responsibilityfor coordinatingthe accounts that we learn from the chroniclers about Inkaic and came in to him from the khipu-keepersof numer- early colonial accountingperiodicities and prac- ous, differentayllus. All of this informationwas tices.14 then synthesizedinto the single summaryaccount- The second point that I want to focus on con- ing knottedinto khipuUR6. cerns a particulargroup-what I would term a This generalinterpretation of correspondences class-of numbers contained in these three among the three Chachapoyakhipu implies that accounts. The two such three-termsets that are additionalayllu-based khipu accounts may have located within the matchingkhipu we have been existedfrom which the groupsof workersassigned examining(Figure 9) are:20-61-20 and 11-35-20. to the other20 monthsrecorded in UR6 weredrawn The firstof these three-termnumber sets is found up. We have studiedclosely the otherkhipu found in Table1, Sectionc, at the end of line two; the sec- at Lake of the Condors,but have not to date iden- ond set is at the end of the highlightedsequence of tified potential"source khipu" for othersegments numbersin Table 1 (i.e., Section c, line 9). As the of UR6. Thismay imply that these ayllu-level khipu numericalvalues in thehighlighted section of Table records were perhaps stored with the ancestral 1 reveal,these two three-termnumber sets contain mummiesof the otherayllus from the region and valuesthat, while not largeby an absolutestandard, Label MatchMatch
Identity Exact Close Legend 1 .----,:;
AB AB MB AB - : :
colorMB MB MB MB:AB ABMB:AB MB MB MB MB MB MB AB MB MB AB AB MB MB KB MB AB MB MB GG MB MB:AB KBMB AB MB MB MB GG MB GG MB AB RL GG AB MB MB AB AB MB MB AB MB KB GG MB MB MB RL
1 1 2 1 1
value1 1 1 1 1 1 1 1 1 8 1 2 8 6 2 5 1 2 14 2 1 8 4 3 1 2061 20 1 2 1 1 1 1 1 1 1 1 1 1 2
att V U V V V V V V V V V R R R R R R R R R V R V R V V R V V V V U V V V V V V V U V V U V V V V V V V V V U V V
UR21 1 1s1 10 11 12 13 14 15 16 17 18 19 cord 2 3 4 5 6 7 8 9 20 21 22 23 24 25 26 27 28 29 30 31 31s132 3334 35 36 37 37s138 39 39s140 41 42 43 44 45 46 47 48 48s149 :50
AB MB : : color MBMB MB MB VR MB MB MB MB MB MB MB MB MB MB MB MB MB MB MB GG MB KB MB MB MB MB GG MB MB MB VR MB MB MB MB VR MB MB MB MB MB MB MB MB MB MB MB MB KB MB KB 1
2 1 8 4 3 1 20 6120 1 14 value 2 1 1 2 2 8 1 2 9 2 5 1 2 7 14 2 1 3 2 3 2 1 16 att V V V V V V V V V V V V V V V V V V V V V R R R R R U V R R R V V V V V V V V V V V V V V V U V V V U V
UR6 cord 256257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 LP12s1 LP12s2LP12s3LP12s4 LP12s5 LP12s5s1 LP12s6 LP12s7 LP12s8LP12s9 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 291s1 292293 294 294s1 295
MB MBMB MB MB ABAB MB AB MBAB MB GG : : : : : : : : : : : : : color MBMB MB MB VR MB AB AB MB MB AB KB RL KB MB AB AB RL GG MB KB RL GG AB AB RL MB RL GG RL KB AB MB MB AB MB MB MB MB MB AB MB MB MB MB MB MB KB MB MB MB MB
1 1 value 12 1 2 2 8 1 2 8 7 2 5 1 2 14 2 1 8 4 3 1 2061 20 1 1 2 1 3 2 4 16 2 1
att R V R R U R R R R R R U V R R R R R R R R R V R R R U R R R R R U R R R R R R R R R R R R R R R U R R R
UR9 cord 143142 141 140 139 138 137 136 135 134 133 132 131 130 129 128 127 126 125 124 123 122 121 120 119 118 117s1 117116 115 114 113 112 111 110 109 108 107 106 105 104 103 102 101 100 99 98 97 96s196 95 94 AB AB AB AB AB : : : : :
MBMB MB GG KB MB AB KB GG MB GG MB MB GG MB GG MB AB MB MB GG MB MB GG MB AB KB RL GG AB MB KB MB AB MB MB MB GG AB MB KB KB AB MB MB GG AB MB AB MB AB MB GG MB GG AB MB GG KB AB MB GG
13 1 1 1 1 3 1 1 1
1 14 4 1 1 4 1 1 5 1 1 1 1 1 1 1 2 1 1 1 1 1 4 5 9 1 1 1 3 8 2 3 2 1 3 1 5 1 1 1 10 9 1 1 1 1 1 1 1 1 1
V V U V V V V V V V V R V U V U V V U V V V V U V V U V V V V V V V V V U V V V V V V V V V V V V V V V U V U V V V V V V U
51 52 52s153 54 55 56 57 58 59 60 61 62 62s163 63s164 65 65s166 67 68 69 69s170 71 72 73 74 75 76 77 78 79 80 81 81s182 83 84 85 86 87 88 89 90 91 92 93 94 95 96 96s197 97s198 99 100101 102 103 103s1
MB AB KB AB MB AB : : : : :
ABMB GG KB MB AB MB MB GG AB KB GG VR KB MB MB KB VR MB AB MB MB MB AB MB KB MB AB AB MB KB MB KB MB KB GG KB KB AB MB MB GG MB KB KB MB KB KB MB MB MB VR MB AB MB MB VR MB AB MB MB MB
4 1 1 1 3 2 1 3 1 5 1 1 1
4 2 1 1 1 2 1 1 4 7 1 2 1 3 11 10 3 3 1 1 10 9 2 2 3 2
V V V V R R R R V R R V V V V V V V V V V V V V V V V V U V V U V V V V V R R R R V R R R V U V U V V V R R R R R R R R R R
296297 298 LP13s1 LP13s2LP13s3 LP13s4 LP13s5 LP13s6 LP13s7 LP13s8 LP13s9 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 314s1 315 316 316s1 317 318 319 320 LP14s1 LP14s2LP14s3 LP14s4 LP14s5 LP14s6 LP14s7 LP14s8 LP14s9 321 321s1 322 322s1 323 324 325 326 327 328 329 330 331 332 333 334 335
MBAB AB MB MBGG MB KB MBMB MB MBMB MB : : : : : : : : : : : : :
MBMB GG GG: GG KB KB MB AB MB MB GG AB GG AB MB AB MB MB MB AB MB MB MB AB MB MB AB MB MB MB MB MB MB GG GG AB MB MB MB MB MB GG AB KB AB MB MB MB MB MB VR MB AB MB MB MB MB MB MB KB GG
14 1 1 3
4 2 1 1 4 1 5 1 1 2 1 1 4 7 11 1 2 1 3 10 4 3 2 1 3 5 1 2 3 2 7 1 3 11
U R R R R V R R R R V U R R R R R R R R R R R R R R R V R U R R U R V V V R R R R R V R V V R R V V V V V V V V V V V V V V
93s193 92 91 90 89 88 87 86 85 84 83s183 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66s166 65 64s164 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36
Figure 9. Three matching khipu from Lake of the Condors.7 AB W AB AB AB : : : : :
MBAB MB AB MB GG MB GG AB MB GG KB AB MB GG MB GG AB AB GG KB MB GG AB AB MB KB AB AB AB MB BL KB KB KB AB AB AB MB MB MB MB GG MB AB AB MB GG AB AB AB AB AB AB AB MB AB
1 1 1 1 1 1 1 10 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 1 2 9 1 1 1 6 3 7 6 6 1 5 11 5 1 1135 20
V V V V V U V U V V V V V V U V U R V V R V U V R V V V V V V V R R R V V R R U R R R R R R R R V V V V V V R V V
92 93 94 96 96s197 97s1 99 100101 102 103 103s1 104104s1 106 107 108 109 109s1 110111 112 113 114 115 117118 119 120 121 122 123 124 125 125s1 126127 128 129 130 131 132 133 LP1 LP1s1 LP1s2LP1s3 LP1s4 LP1s5 LP1s6 LP1s7 LP1s8
95 98 105 116 AB MB MB : : :
KBMB MB MB VR MB AB MB MB VR MB AB MB MB MB MB MB MB MB MB MB KB KB MB KB GG KB MB MB MB MB MB GG GG MB KB 1
1 6 1 5 1 5 1 1135 20 1 10 9 2 2 3 2 7 1 3 1 1 1 6 115 7 5
V U V V V R R R R R R R R R R R R R R R R R R R R R R R R R U U R R R R
322322s1 323324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 LP15s1 LP15s2LP15s3LP15s4 LP15s5 LP15s5s1 LP15s6 LP15s7 LP15s8LP15s9 539
MBMB AB : : : MBMB MB MB VR MB AB MB MB MB MB MB MB KB GG MB MB MB GG GG GG MB MB MB MB MB MB MB MB MB MB MB MB AB MB MB MB MB MB MB MB AB MB MB MB MB MB MB MB MB MB MB MB AB AB MB MB AB MB
EE 1 1 1 2 3 2 7 1 3 11 1 1 6 5 7 5 1 1 1 1 1 3 1 3 2 1 3 2 3 7 2 1
R V V V V V V V V V V V V V V V V V R V R V R U R U U U U U R R R V V V V V U V V V V V R U R U R R R R R V V R V V V
50 49 48 47 46 45 44 4342 41 40 39 38 37 36 35 34 33 32 31 3029 28 27s127 26s526s4 26s3 26s2 26s1 26 25 24 23 22 21 2019 18s118 17 16 15 14 13 12s112 11s111 10 9 8 7 6 5 4 3 2 1 Urton] KHIPUARCHIVES 163 are nonetheless notably larger than the values we find the set (12, 35, 20) / (11, 35, 20); and in recordedelsewhere in Section c (i.e., in the area Sectiond thereis the set (10, 30, 10) / (10, 30, 10). thatcontains the matchesbetween UR6 andKhipu What could have been the meaningand signif- UR9 and UR21). To be clear,the three-termval- icance in the Lakeof the Condorskhipu archive of ues I am discussing are numericalvalues knotted the 10 three-termnumber sets andtheir "pairing," into groupsof three adjacentcords. as suggestedabove? In the firstplace, if the three- As seen in Figure 9, the firstof the three-term termnumber sets are, indeed,identity labels, then sets mentionedabove (20-61-20) is also found in we must remove these as values in any tribute UR9 andUR21; they arethe sets of valueson three accounting, or assessment in Khipu UR6. This stringsindicated by shadingin the uppersection of would clearly call into questionmy interpretation numericalvalues recorded from each khipu.As for that the total knot count, includingknot values on the second of the three-termnumber sets (11-35- the "identitylabels," on this khipu,pertained to an 20), versions of this appearat the ends (bottoms) accountingof ca. 3,000 mit'ayocin the Lakeof the of the columns for UR6 and UR21 in Figure 9. Condors region. That is, removing the identity Khipu UR9 does not terminatein a comparable labels as mit'ayoc counts produces annual (i.e., three-termnumber series. However, the threefinal two-year) counts of 1,513 (= Year 1) and 601 (= stringsof this khipu are crinkledand twisted in a Year2), for a two-yeartotal of 2,114. This revised mannersuggesting that each of the stringswas pre- total is well beyond two of the standardwaranqa viously knotted.Therefore, I think that UR9 may (1,000) accountingunits and is not (to my knowl- also at one time have ended in the three-term edge) close to a tributarycount recordedin colo- numericalset 11-35-20. nial documentsfrom this region.Given the present What can have been the significance, or the uncertaintyin ourknowledge of thereferents of the meaning,of the three-termnumber sets identified accounts composing the Chachapoya (or any above?In orderto addressthis question, we should other!)khipu archive, we mustbe contentto allow look again at all of the numericaldata encoded in both interpretations-i.e., that UR6 representsan KhipuUR6, as these are displayedin Table 1. By accountingof ca. 3,000 mit'ayuq,or that it is an looking at the underlinedvalues, we see thatthere accountingof 2,114 of somethingwith 10 identity are,in fact, 10 three-termnumber sets spreadacross labels-to standas equal possibilities. this khipu.(The bottom-mostof these numbersets If we do, however,pursue the implicationsof appearsto be composedof five numbers[10-1-30- the three-termnumber sets as labels, or names, I 2-10]; however,the secondand fourthnumbers in ask: could these perhapshave representedlabels this series [i.e., 1 and 2] are tied onto subsidiary thatidentified the social groups-e.g., ayllus-that strings,which means thatif we just read the val- occupiedthis areain late prehispanicto earlycolo- ues on the threeadjacent pendant cords, they con- nial times?(The Chilchos ethnic group was divided tain the three-termnumber set: 10-30-10.) Five of into some nine ayllus [Espinoza Soriano 1967; these number sets in Table 1 are located within Lerche 1995].) Perhapsthe labels in UR6 identi- each half of the two-yearcalendar of UR6. Table fied a collection of local ayllus. In this regard, 2 presentsthe three-termnumber sets in theirloca- Lerche(1995:58-6 1) has arguedthat a moietyorga- tions within the overallstructure of UR6. nizationwas commonamong various ethnic groups I advancethe hypothesisthat these 10, three- in the Chachapoyasregion. Thus, I wouldask if the term number sets representlabels, or emblems, pairingof three-termnumber sets suggestedabove relating to the information recorded on Khipu could indicatethe existencein this accountof ayllu UR6.15 In this regard,I notethat all 10 of these sets organizedinto upper (hanan) and lower (hurin) occur on the final three stringsof loop pendants. moieties (see Fossa2000 on thispoint). Or perhaps Thus, loop pendantsappear to have been the car- the three-termnumber sets identified tasks that riersof identitylabels, whatever the lattermay have were to be performed during the calendrical signified. Furthermore,several of the three-term period(s)in question,or the labelsof temporalperi- number sets appear to representpaired sets; for ods (e.g., seasons)themselves during the two-years example,in Section a, we find the possible paired recordedin KhipuUR6. Whatevertheir referents, set (30, 65, 20) /(30, 80, 20); in Sections b and c these three-termnumber sets appearto represent 164 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005 the firstidentifiable examples of "names,"or labels, archives of interrelated,cross-referenced khipu recordedon khipu.16 from differentregions around the empire. The second observationand conclusionis that Conclusions a few of the matchingkhipu examined herein sug- gest that we may be able to recognizekhipu that Wherehave the data,observations, and interpreta- are relatedto each other in relativechronological tions presentedin this study taken us in terms of terms,as in the negotiationof accountsover time. ourattempts to understandthe procedures and prac- This featurehas been seen in those exampleswith tices of encoding and decoding information in close, thoughnot exact, matches.I have suggested archives of Inka khipu? I think there are several that a couple of these may representsuccessive implicationsand conclusions we can drawthat will accountsof the same accountingtask performed at help move us along towardour ultimategoal of two differentpoints in time, or as recordedby two decipherment-or at least of determiningwhether differentkhipu keepers who saw or hearddifferent or not these perplexingknotted string records are, accounts of a body of data for which they bore in fact, decipherable. equal responsibility.The hope of being affordeda The first implicationis that Garcilaso'sobser- view into the negotiationof accounts over time vations with respect to the existence of multiple promises to considerablydeepen, and problema- khipu that recordedsimilar-or, as he says, "the tize, our view of khipu accounts and accounting same"-informationcan now be confirmed,at least practices. at a generallevel. One of the mostintriguing reflec- In this regard,we can make anotherinteresting tions on the informationpresented herein is that comparisonto bookkeepingprocedures that appear these examples of duplicate and overlapping in the earlycuneiform tablets from Mesopotamia. accounts are similar to bookkeepingprocedures Nissen et al. (1993) point out thatthere are several evidencedin the earliestknown state-levelsystem examples of tabletslinked to each other in terms of accounting-that of the cuneiform tablets of of the balancingof debits with credits and of the ancient Mesopotamia(e.g., Steinkeller2003:42). postingof accountson some productor activityin As Nissen et al. (1993:30) note in their study of consecutiveyears. In such examples, the amount early bookkeeping techniques in Mesopotamia, of goods posted in a debit tablet (or in one year) "[t]he tablets were seldom isolated information only approximatesthe amountposted in a credit transmitters;rather, they almostwithout exception tablet (or in the next year; Nissen et al.1993:43). representa part of runningbook-keeping proce- Such credit/debit(or successive annual)postings dures in which pieces of informationfrom one could account for the kinds of "close matches" tablet were transposed to another."Replacing between khipu that we have encounteredin this "tablet"with "khipu"in this quotationgives an study (e.g., see Figures5 and 6). only slightly overstated characterizationof the The thirdobservation involves a matterthat has place of duplicationin prehispanicAndean record been the subjectof considerablespeculation and keeping as it was characterizedby Garcilaso.For controversyin recentyears. This is the questionof example,this quotecalls to mindthe kind of match- the degree to which any two khipu keepers may ing accountsseen, for instance,in Figures2, 3, and have been able to interpret,or read, each other's 9 in which informationrecorded in one or two khipuaccounts. The issue here is raisedby a mid- khipuappears to be reproducedin another,usually seventeenth-centurychronicler of Inkahistory and largerone. These examplesof matchingand over- culture, Bernab6Cobo. In characterizingkhipu lapping khipu make it imperativethat we devote record-keepingprinciples and procedures,Cobo more effortthan has been expendedto date build- madethe following quite novel (see Urton2002:17) ing up a corpusof matchingkhipu and thereby both statement: expanding and deepening our understandingof what must have been a central feature of khipu [N]ot all the Indianswere capableof under- record-keepingpractices in the Inka empire. In standingthe quipos;only those dedicatedto short,we now have the prospectof, as well as the this job could do it; and those who did not mandate for, beginning to identify and collate studyquipos failed to understandthem. Even Urton] KHIPUARCHIVES 165
amongthe quipo camayos themselves, one was ies focus on khiputhat are complete(or relatively unableto understandthe registers and record- so) andfor which one may makedeductions regard- ing devicesof others.Each one understoodthe ing the arithmeticor mathematicaloperations that quiposthat he madeand what the otherstold may have been employed in calculatingthe data him [Cobo 1983 (1653):253-254]. recorded,or in searchingfor numericalpatterns, rhythms,etc. Such studies have addedimmeasur- Accordingto Cobo'saccount, one mightexpect ably to ourunderstanding of the khipuaccounting thatany given khipu was readableonly by thekhipu system;however, this has come atthe price of leav- keeperwho made thatparticular one (see the dis- ing asideor pushing into thebackground the analy- cussion of this issue in Urton2003:19-26). How- sis of samples that are not of immediate ever,the examplesof matchingkhipu presented in mathematicalinterest, or thatare incomplete.The this paperrender this view highly untenable.That archival approachto khipu studies (which still is, is it reasonableto thinkthat the makersof the allowsfor mathematical studies) is premisedon the three Puruchucokhipu discussedabove (see Fig- notion that all khipu, no matterhow fragmentary ure 7) were unable to read or interpretthe infor- or incomplete, should be studied and their data mationin each other'skhipu? Or can we presume thoroughlyrecorded (see Radicatidi Primeglio's that the two Chachapoyas khipu keepers who [1964:9] encouragementon this point). A khipu retainedUR9 and21 wereunable to readand inter- fragment-even one bearingonly a few cords- pretthe portionof UR6 thatso closely matchedthe may match anothersample, and the two together informationin theirown records(see Figure9)? I may give us important,unique insights into the believe the informationpresented herein renders organizationof Inkapolitical economy andrecord Cobo's insistenceon the absenceof some level of keeping at local, regional,and state levels. Pursu- conventionalityin the khipuunsupportable. ing the strategyof recordingall informationon The fourthimplication concerns the three-term every extantkhipu, no matterhow incompleteor numberunits identifiedin the Chachapoyakhipu, fragmentary,may allow us to re-assemblethe long UR6, 9, and21. Whatcan these number series have fragmentedarchives of this extraordinaryancient meant?How might they have been interpretedin Americanaccounting system. this particularaccounting context? Can the three- termnumber units have perhapsbeen logograph- like sign units, which identifiedgroup (e.g., ayllu) Acknowledgments. Thanks to Carrie J. Brezine, Galen identities?Might they haveinstead indicated tasks Brokaw, FrankSalomon (the latter two of whom were self- to be undertaken,or the times in which such tasks identified reviewers for Latin AmericanAntiquity) and R. T. Zuidema for and invalu- shouldbe Giventhe state reading, commenting on, making performed? rudimentary able suggestions for improvementson an earlier draft.I am of ourunderstanding of suchterms and of theirpos- responsible for all errors that remain. Thanks to my wife, sible pairing within and across the two years Julia Meyerson, who preparedall but one of the illustrations accountedfor in Khipu UR6, we cannot be too (Figure 9 was preparedby Carrie Brezine). Thanks also to Luis Villacorta for his and insistent on any one of the Felipe help, encouragement, interpretation signifi- immense will in of researchin Peru. cance of these emblemsor labels. What- good support my Lima, apparent Thanksto the following individualswho helped make possi- ever we finally determine with regard to the ble my researchin various khipu collections: to Dr. Enrique intended referent(s) of these three-termnumber Gonzales Carr6and Ms. Rossana Mendoza Neyra for work sets, they appearto offer an intriguingset of char- at the site museum at Puruchuco,Lima, Peru;to Dr. Manuela Fischer and Dr. Marie Gaida for work at the Museum actersfor futurestudy. ftir in to Dr. Morris and Vuka the most Vlkerkunde, Berlin; Craig Finally,perhaps importantimplication Roussakis for work at the American Museum of Natural of the materialpresented here and especially of the History, in New York;and to Dr. Sonia Guillen and Adriana "archival"approach to khipu studies for which I von Hagen for work at the Centro Mallqui, Leymebamba, have arguedis the encouragementto recordinfor- Chachapoyas,Peru. I acknowledge with deep gratitude the mationon all extantkhipu, no matterhow incom- financial support provided by the following institutions or foundations:the National Science Foundation SBR- be. In the there has been a (grants: plete they may past, 9221737 and BCS-0228038), the HarvardUniversity Faculty decided tendencyon the partof khipuresearchers of Arts and Sciences, and the John D. and Catherine T. to studyonly those khiputhat "add up." Such stud- MacArthurFoundation. 166 LATINAMERICAN ANTIQUITY [Vol. 16, No. 2, 2005
References Cited nomicAdministration in the Ancient Near East. Univer- sity of ChicagoPress, Chicago and London. Ascher,Marcia Nordenskiild,Erland 2002 Reading Quipus: Labels, Structure,and Format.In 1925 The Secret of PeruvianQuipu. ComparativeEthno- NarrativeThreads: Accounting and Recounting in Andean graphicalStudies. 6, Part 1. Goteborg. Khipu, edited by Jeffrey Quilter and Gary Urton, pp. Polo de Ondegardo,Juan 87-102. Universityof TexasPress, Austin. 1916 [1571] Los erroresy supersticionesde los indiossaca- Ascher,Marcia, and RobertAscher dos del tratadoy averiguaci6n que hizo el Licenciado 1975 The Quipuas a Visible Language.Visible Language Polo. Colecci6nde Librosy DocumentosReferentes a la 9:329-356. Historiadel Peril,Vol. 3. Imprentay LibreriaSan Marti, 1978 Code of the Quipu:Databook. University of Michi- Lima. gan Press,Ann Arbor (Available at: http://instructl.cit.cor- Radicatidi Primeglio,Carlos nell.edu/research/quipu-ascher/). 1949-50 Introducci6nal estudiode los quipus.Documenta: 1988 Code of the Quipu:Databook II. Marciaand Robert Revista de la Sociedad Peruana de Historia 2 Ascher, Ithaca, New York (Available at: (1949-50):244-339. http://instructl.cit.cornell.edu/research/quipu-ascher/). 1964 La "seriacidn" comoposible clavepara descifrarlos 1997 Mathematicsof the Incas: Code of the Quipu. Dover quipusextranumerales. Biblioteca de la SociedadPeruana Publications,New York. de Historia.Monographs, No. 6. UniversidadNacional Cobo, Bernab6 Mayorde San Marcos,Lima. 1983 [1653] History of the Inca Empire.Translated and Salomon,Frank edited by Roland Hamilton.University of Texas Press, 2002 PatrimonialKhipu in a ModernPeruvian Village: An Austin. Introduction to the 'Quipocamayos' of Tupicocha, Conklin,William J. Huarochiri. In Narrative Threads: Accounting and 2002 A Khipu InformationString Theory. In Narrative Recountingin Andean Khipu, edited by Jeffrey Quilter Threads:Accounting and Recountingin Andean Khipu, and GaryUrton, pp. 293-319. Universityof TexasPress, editedby JeffreyQuilter and Gary Urton, pp. 53-86. Uni- Austin. versity of TexasPress, Austin. Schjellerup,Inge R. Espinoza Soriano,W. 1997 Incas and Spaniards in the Conquest of the 1967 Los sefioriosetnicos de Chachapoyasy la alianza Chachapoyas.GOTARC Series B. GCthenburgArchaeo- hispano-chacha.Revista Hist6rica 30:224-322. logical Theses, No. 7. National Museum of Denmark, Fossa, Lydia G6thenburg. 2000 Two Khipu,One Narrative:Answering Urton's Ques- Steinkeller,Piotr tions. Ethnohistory47:453-468. 2003 ArchivalPractices at Babyloniain the ThirdMillen- Garcilasode la Vega, El Inca nium. InAncientArchives and Archival Traditions, edited 1966 [1609-1617] RoyalCommentaries of theIncas. Trans- by MariaBrosium, pp. 37-58. OxfordUniversity Press, lated and with an introductionby HaroldV. Livermore. Oxford. Universityof Texas Press,Austin. Urton,Gary Guevara-Gil,Armando, and FrankSalomon 1994 A New Twistin an OldYam:Variation in KnotDirec- 1994 A 'PersonalVisit': Colonial Political Ritual and the tionalityin the InkaKhipu. Baessler-Archiv Neue Folge, Makingof Indiansin theAndes. ColonialLatin American Band XLII:271-305. Review3:3-36. 1997 TheSocial Life of Numbers:A QuechuaOntology of Guillen, Sonia E. Numbers and Philosophy of Arithmetic. University of 1999 Arqueologiade emergencia:inventario, catalogaci6n TexasPress, Austin. y conservaci6nde los materialesarqueol6gicos de los mau- 2001 A Calendricaland DemographicTomb Text from soleos de la Lagunade los C6ndores.Final report submitted NorthernPeru. Latin American Antiquity 12:127-147. to the InstitutoNacional de Cultura,Lima. 2002 RecordingSigns in Narrative-AccountingKhipu. In Julien,Catherine J. NarrativeThreads: Accounting and Recounting in Andean 1988 How Inca Decimal AdministrationWorked. Ethno- Khipu, edited by Jeffrey Quilter and Gary Urton, pp. history35:257-279. 171-196. Universityof TexasPress, Austin. Lerche,Peter 2003 Signsofthe InkaKhipu: Binary Coding in theAndean 1995 Los Chachapoyay los simbolosde su Historia.C6sar Knotted-StringRecords. University of TexasPress, Austin. Gayoso, Lima, Peru. 2005 Carlos Radicati di Primeglio: Patron of Peruvian 1999 A GraveCase of Robbery.Geographical 71:18-23. QuipuStudies. An Introductionto the Re-editionof Works Locke, L. Leland by C. Radicatidi Primeglio.Universidad Nacional Mayor 1923 TheAncient Quipu, or PeruvianKnot Record. Amer- de San Marcos,Lima, in press. ican Museumof NaturalHistory, New York. Urton,Gary, and CarrieJ. Brezine Mackey,Carol 2005 InformationControl in the Palaceof Puruchuco:An 1970 KnotRecords inAncient and Modern Perl. Ph.D.dis- AccountingHierarchy in a KhipuArchive from Coastal sertation,University of California,Berkeley. University Peru. In Power in the Inka Empire, edited by Richard Microfilms,Ann Arbor. Burger,Ramiro Matos M., and CraigMorris. Dumbarton Matienzo,Juan de Oaks,Washington, D.C., in press. 1967 [1567] Gobierno del Peri, edited by Guillermo von Hagen,Adriana LohmanVillena, Travaux de l'InstitutFrangais d'ltudes 2000 Nueva iconograffaChachapoyas." iconos: Revista Andines,Vol. 11. Lima. peruana de conservacicin,arte y arqueologia4:8-17. Nissen, Hans J., PeterDamerow, and RobertK. Englund von Hagen,Adriana, and Sonia Guillin 1993 ArchaicBookkeeping: Writing and Techniquesof Eco- 1998 Tombswith a View.Archaeology 51(2). 2:48-54. Urton] KHIPUARCHIVES 167
Notes on AS 174 (see the discussion of these relatedkhipu samples in Ascher and Ascher's Databooks [on-line resource; see 1. The khipu databasethat we are currentlydeveloping at above, Note 5] underAS98, Note 5). Thus, khipuAS 174 may Harvard is a searchable database (see website at represent an additional matching-i.e., "checks and bal- http://khipukamayuq.fas.harvard.edu/).I would note that the ances"-account vis-ai-visthe pairAS 173 andAS 159. databasecreated by the Aschers (1978, 1988), which is the 9. Thanks to Frank Salomon, who reminded me of the most importantand valuableresource to date for khipuschol- valuable informationon Mesopotamianaccounting methods ars, is in PDF formatand is not, therefore,searchable by elec- presented in the wonderful book by Nissen et al. (1993), tronic means. The Aschers' tables also do not include Archaic Bookkeeping. informationon such khipu constructionvariables as direc- 10. The relevantcolor codingsfor the threekhipu in Figure tionality of cord spin/ply or directional variation in cord 7 in Mackey's(1970) color nomenclatureare as follows: attachmentand knotting(see Urton 2003:56-57). Monochrome bi-/multi-color 2. Thanksto GarethCook of the Boston Globe for several C = light brown 2 = black and white additionalreferences to matchingkhipu (he informedme that G = blue 4 = green and white he had learnedof them from MarciaAscher). B = white 10= blue and white 3. I recently publisheda book outlininga binarycoding- A = brown based theory on the encodingand decoding of informationin 11. It is not commonly understoodby those not directly the Inka khipu (Urton 2003). That theory,which I presented involved in khipu studies that it is, in fact, often extremely clearly as a hypothesisfor furthertesting and analysis,is now difficult to read, or interpret,khipu knots. This is especially in the public domainand will stand,fall, or be modifiedunder true when single knots are tied closely togetheron very thin critiques,challenges, support,etc. that it receives from other cords; similarly,on loosely spun, very hairycords, it is often scholars,as well as appropriatetesting by the KhipuDatabase virtuallyimpossible to determinethe exact numberof turnsin project.The point is, the presentstudy reflects very few of the a tightly tied long knot. methodologicalapproaches and theoreticalstances developed 12. From what I have learned from museum notes and in my book on binarycoding. I am emphaticallynot rejecting from Dr. Sonia Guillen's (1999) salvage reporton the recov- thattheory, but neitherdo I intendto be limitedto the ideas and ery of the materialfrom Lake of the Condors, Khipu UR6 approachesdeveloped in thatpublication. Thus, in the present was found in Chullpa3 at the site of LC1 (i.e., the main rock study,I take up anotherbody of informationand anotherline overhang on the cliff face directly above Lake of the of approach-without prejudiceto my earlier work-on the Condors). Khipu UR9 was also found in LCI, but within perenniallydifficult problem of interpretingthe Inkakhipu. Chullpa4. As far as I am aware,the whereaboutsof the third 4. To the best of my knowledge, the firstperson to argue sample, UR21, at the time of its recoveryis not recorded. explicitly in favor of an "archival"approach to khipu studies 13. The numericalvalues of knots on KhipuUR6 reported was Radicati di Primeglio(1964:9). His study was based on in an earlierpublication (Urton 2001:141, Figure 9) contain six samples recoveredfrom the Santa River Valley.Radicati two errors. These occur in the last pendant/loop pendant di Primeglio's appealfor a study of all khipu samples from a grouping(i.e., the bottom set of 21/9 cords in Year2, Section given site, no matter how incomplete or fragmentary,was d). The correctvalues should read as follows: (a) for this set made in direct oppositionto Nordenskiild (1925). With his of 21 pendants,the value is 12 (ratherthan the reported26), preoccupationfor the study of astronomicaland calendrical and (b) for the loop pendant,the value is 37 (ratherthan the periodicitiesin the khipu,Nordenskiold asserted that it made reported 66). The correct values are given in Table 1 (see sense only to study completekhipu. below, in text), last two lines in Section d. These corrections 5. The Aschers' khipu tables are available online at: change the total knot count from the 3005, reportedin 2001, http://instruct1.cit.cornell.edu/research/quipu-ascher/ to 2962, as reportedherein. This correctionwill obviously 6. The conventionin the field of khipu studies is for the affect the interpretationof the astronomicaland calendrical first investigatorof a sample to assign an investigatoridenti- significance of numerical values recorded on UR6 as dis- fication label (e.g., AS = Ascher, UR = Urton), along with a cussed in that earlierstudy (Urton2001:140-143, Table 2). unique numberfor each sample.Although it is common prac- 14. Thanksto R.T. Zuidemawho suppliedme with these tice to have only one readingof a khipu, and for subsequent referencesto the four-monthperiodicity of accountingin Inka researchers to add informationto the existing description and early colonial Cusco. (e.g., see Urton 2003:58), the conventionof assigningunique 15. MarciaAscher (2002) has discussed, in generaltheo- investigator labels and numbers also allows subsequent retical terms, the use of khipu numerical values as labels, researchers to produce, and distinguish among, multiple, ratherthan as magnitudes. independentreadings of samples. 16. In an earlierstudy (Urton2002), I discussed the exis- 7. Color abbreviations,terms, and the notationfor com- tence of severalhundred instances of three-term"anomalous" bining colors follow the system of Marciaand RobertAscher numerical values that appear on a khipu from Chancay- (1978, 1988), as explainedin the introductionsection of their B/8705-in the AmericanMuseum of NaturalHistory, in New website, http://instructl.cit.cornell.edu/research/quipu- York.It will be importantin the futureto analyze the relation- ascher/contents.htm ship between the three-termnumber series in Chachapoyas 8. It should be noted that AS159 and 173 were each with those on the AMNH samplefrom Chancay. loosely tied to other khipu at the time of their study.AS159 was tied to AS160 and AS173 was tied to AS174. Sums of SubmittedFebruary 16, 2004; Accepted June 17, 2004; values on certain groups of pendantson AS173 are recorded Revised February23, 2004.