The Archaeology of Measurement

Comprehending Heaven, Earth and Timein Ancient Societies

Edited by

fain MorleyIGble College, Oxford.

Colin RenfrewThe McDonald. Institwte for Archaeologicnl Research

CavrnnrDGEUNTVERSITY PRESS alwlnl-X / d oto

5

Recording measure(ment)s inthe Inka khipu

Gnry Urton

lntroduction

The objective of this chapter is to explore variousfeatures of the encoding of information in the hhipw

(Quechua: 'knot'), the knotted-string device used forrecord keeping in the Inka empire of pre-ColumbianSouth America. Specifically, I rvill discuss what the tes-

timony concerning khipus contained in Spanish colo-nial documents) as well as study of museum samples ofkhipus, can teach us about the types and standards oflreasurerrents used by local and state administrators inthe Inka empire. Given these objectives, rve should be

clear from the beginning about the range of concepts

and practices connected with 'measure' and 'measure-ment') at least as these are understood in English. Tomeasure means "to compute, estimate) or ascertain theextent, quantity, dimensions, or capacity of [something],especially by a certain rule or standard" (Webster\ New

Tiventietb Centwry Dictionary 1978).In addition to thisdauntingly rvide range and variety of activities, mea-

surement involves more abstract concepts and forms ofevaluation, including "to estimate by reference to any

standard; to judge of the value, extent, magnitude, orgreatness of [something/someone]" (Webster\ New

T)r,entieth Centwry Dictionary 197 8).

Clearly, if our objective here is to discuss the record-ing of measure (ment)s in the Inka khipus, we will have

to find some way to limit the domains of reference, as

space rvill not permit a full consideration of the many

and varied principles and activities evoked previously.In fact, there is no need to reduce the subject matterartificially, for lve are faced from the outset rvith a fun-damental limitation to our knowledge of and ability tointerpret information in these devices. The limitationresults from the unfortunate circumstance that rve have

not ),et achieved a complete decipherment of the khipus.

54

While we can interpret certain signs encoded in these

devices, we cannot read the entire messages.

To be somewhat more specific, Spanish observers

of colonial era manipulations of khipus inform us thatthe knotted records contained at least two basic types ofinformation, or sign values: signs standing for numbers

and signs standing for identities (i.e., names of people,

places, things). While we have known for almost a cen-

tury how to read khipu numerical sign values in con-

figurations of knots (Locke L923), we do not know inmost cases how to interpret the signs used to signifyidentities. For example, while we might determine that a

specific cord contains knots signing the numerical value

'36', we generally cannot say rvith certainty lvhat such a

number referred to - lvhether to a dimension of a culti-vated field, the result ofa census count) or another formof measurement. Only in the case of khipus containingeither data from astronomical observations organizedand recorded in calendrical periodicities (see lJrton200I) or data recorded in the full decimal values used inInka tribute assignments (see later discussion) can rve be

relatively certain of the referents of numerical informa-tion recorded on khipus. It is important to note in thisregard that what we take to be number signs may in some

cases have been interpreted as signifiers ofidentities, as

when numbers were used as labels, rather than as mag-

nitudes (see Ascher 2002; Urton 2003 and 2005; Urtonand Brezine 2005).r Unfortunately, it is not alrvays clear

when any given knot configuration recorded on a khipuwas meant to be read as a number label rather than as a

magnitude; research on this matter is controversial and

ongolng.Given the circumstances outlined, the question

arises, What can we say about different types of mea-

surements that might have been recorded on khipusfWe can discuss two types of information with a con-

siderable degree of confidence. First, we can detailwith considerable specificity rvhat the Spaniards whoobserved khipus in use in the early years follorving theconquest (beginning in 1532) had to salr

"6o.r, .n.

measurements Inka officials recorded on them. And,second, we can analyze numerical data registered onextant khipu samples. We will find from these twosources of information that we are in fact able to make

a number of quite specific suggestions about differenttypes of measure(ment)s that were registered on khipusby local and state administrators.

Before entering into discussions of the various types

of data outlined previously, it may be helpful to those notfamiliar rvith the Inka khipu to give a brief overview ofthe structural features and visual characteristics of these

remarkable devices.

Recording measure(ment)s in the lnka khipu 55

Khipus and their methods ofinformation registry

According to my own inventory, there are 750+/- khiptsamples currently in museums and private collectionsin Europe, North America, and South America. Whilesome khipus are too fragile to permit study, some 375samples have been studied closely, and observations onmany of the se may be viewed at http://khipukamayuq.fas.harvard.edul Statistical information pertaining tokhipu structures discussed later derives from analyses ofdata by the Khipu Database project, Harvard University,the home of the Web site noted.2

Khipus are knotted-string devices made of spunand plied cotton or camelid fibers. The colors displayedin khipus are the re sult of the natural colors of cottonfiber and camelid hair or of the dyeing of these mate -

rials with natural dyes. The 'backbone' of a khipu isthe so-called primary cord, a ca. 0.5 cm in diametercord to which are attached a variable number of thinnerstrings, called pendant cords (Fig. 6.I). Khipus containfrom as few as one up to as many as I,500 pendants(the average for 350 of the samples studied to date is84 cords). Top cords are pendant-like strings that leave

the primary cord opposite the pendants, often afterbeing passed through the attachments of a group ofpendant strings. lTop cords often contain the sum ofvalues knotted on the set of pendant cords they bindtogether./About one-quarter of all pendant cords have

one or more second-order cords, called subsidiaries,attached to them. Subsidiaries may themselves bear

subsidiaries, and so on, to produce multiple , branchlikestring structures (for an overview of khipu structures)see Conklin 2002).

A BBAA B A B B B

A = Pendant CordsB = Subsidiar/ Cords

The majority of khipus have knots tied into pen-dant, subsidiary, and top strings in tiered clusters ina decimal system of numeration (Locke 1923). Threebasic types of knots make up the decimal signing sys-

tem: figure-8 knots signifying 1s, 'long' knots signi-fying the values 2-9, and single, or overhand, knotssignifying full decimal values (i.e., I0s, 100s, 1,000s).The most thorough and systematic treatment to dateof the numerical, arithmetic, and mathematical prop-erties of khipus is Ascher and Ascher's Mntheru.atics

of the Incas: Cod.e of the Qaipws (1997; see also lJrton2003). The Aschers have shown that the arithmetic andmathematical operations used by Inka record keepers

included, at a minimum, addition, subtraction, multi-plication, and division; division into unequal fractionaland proportional parts; and multiplication of integersby fractions (Ascher and Ascher 1997:151-152). It is

important to note that khipus were used to record, butnot to calculate, numerical values._:Values registeredon khipus were calculated by means of stones, maizekernels, or other such objects manipulated on theground (Polo de Ondegardo l9l7 1157ll:164; Acosta2002:343-344; Garcilaso de la Yega 1966 l\609):124;see also Urton 1998; and Platt 2002) or within whatare called ywpa.nfrs ('counters'). The latter are ceramicor stone objects containing compartments representingdifferent subunits or powers of the decimal numerationsystem (see Gentile and Margarita 1992; Lee 1996;Pereyra 1990; Radicati 2006).

While roughly two-thirds of all khipus studied todate have their knots organized in the decimal mannerdescribed, about one-third of samples bear knots scat-

tered across the cords in a nonclustered, nontiered fash-ion. Researchers are generally of the opinion that such

khipus were not records of decimallybased quantitative data, but rather,that they contained signs for values andidentities consulted in narrative render-ings of myths, life histories, event his-tories (e.9., accounts of battles) laws,and so on (Quilter and lJrton 2002).Such narrative renderings of informa-tion knotted onto khipus would have

employed terms for measurements likethose in the second set of definitionsgiven at the beginning of this chap-ter: representations ofthe value, extent,

End magnitude, or greatness of an event orof the actions of an individual in thehistory of the empire ("The Chankasapproached with a large and ponetfnlarmy").Figure 6.1. Khipu structures.

56 Gary Urton

What kinds of information wererecorded on khipus?

From the Spanish chronicles and documents, we learnthat the khipu keepers - known as khipwkawoywq ("knotmaker/organizer") - recorded information pertain-ing to such things as census data and assessments fromthese of what was owed to the state in the way of labortribute, including military service and service in state

mines; counts of the llama and alpaca herds belongingto the state; and a host of information pertaining tothe production, collection) storage) and redistributionof staple goods (maize, potatoes) etc.) and luxury items(e.g., fine textiles, metals, and raw and worked spon-dylus shell). In addition, the chronicler Garcilaso de laVega noted that the Inka knew a great deal of geom-etry because this was necessary for measuring theirIands, and adjusting the boundaries and dividing them(Garcilaso de la Vega 1966 [1609]:I24). Garcilaso wenton to give a more complete accounting of what was

recorded on those occasions when the Inka conquerednew terntory:

When the Inca had conquered a province he had a

record made on his hnots and beads [i.e., knots] of thepasture lands, high and low hills, ploughlands, estates,

mines of metals, saltworks, springs, lakes, and rivers,

cotton fields, and wild fruit-trees, and flocks of bothkinds, including those that produced wool and those

that did not.All these things and many others he had counted,

measured, and recorded under separate headings,

firstly the totals for the whole province, and then those

for each village and each inhabitant. They measured thelength and breadth of the arable land, the cultivable -

area, and the pasture land. When all the details were

known, a full report lvas made of the whole province.(1966 [1609]:269-270)

When we search the Spanish chronicles and documentsfor more detailed information concerning possible stan-dard units for measuring distance, Iength, or weight, as

well as capacity measures for liquids, grains, and othersubstances, or equivalence values used in the exchange

of produce (e.g., one unit of corn = X units of potatoes),we find very little specific information. Our best sources

on such matters are the lcolonial dictionaries of nativeAndean languages. The objective in discussing selected

data from these sources later will not be to review allknown measures recorded in dictionaries, but rather toidentify a few core measuring values and principles andto see how extant khipus might have been used to recordthem (see Lee 1996; Rostworowski 1960).

According to the Quechua dictionary of GonzilezHolguin (1952 [1608]), the general term for measure-ment was twpw.He glosses the term generally as me asure-

ment of any thing (rned.ida d,e qwnlqwiera cosn). He alsoglosses twpu as league (legwa), a Spanish distance mea-

sure of approximately three miles. However, in her studyof the use of this term as a distance measure in references

to the Inka road system, Sanhueza Toh6 argues that thetapb.was ofvariable length (2004:484 and 486). Tupwniis to measure something with a staff (ttara), or gatge/rule (tnedidn), glosses that suggest the existence ofstan-dard measuring devices. The phrase denoting the titleof the official responsible for measuring land (nllpn) wasallpa tupwh apw, 0 cequeh apw ("measttrer, or the one whopartitions land"). Thus, twpu was a measure of length/distance as well as an areal measure. It is unclear whatthe standard size of an areal tupw was in Inka times orwhether there even was a standard. Rostworowski docu-ments values for the twpw in early colonial sources rang-ing from such measures as 60 x 50 paces to the amountof land required to support a married couple withoutchildren (Rostworowski 1960:15-16). She concludes

that the size of the twpw was variable and depended onthe context of its delineation.3

As for subdivisions of the twpw used as a land mea-

sure, Gonzdlez Holguin notes that half of hwc tupw("one twpw") was the unit called chectfl,; one-quarter of a

tupuwas the sillcw; and one -eighth was the cutruw. Thts,the normative principle of partitioning tupws as reflectedin this terminology was the full twpu unit successively

halved, a process that reflects r,vhat was perhaps the mostcommon organizational principle in the Inka state: dual-ism, or the (repetitive) subdivision of whole units into

"halves. I would note here, as we will find later, that cen-

sus accounting and tribute records were organized on a

decimal principle, that such values and unit groupings donot appear to have been employed in subdividing length,width, capacity, or other such substance measures.

Several Inka measurements were based on bodyparts. Examples include the rikra, which was equated

with the Spanish term braga ("arm"), the distance fromthe midline of the body to the tips of the outstretchedfingers of one arm. Rikrn also indicated the capacitymeasure of an arm load. Another body part measure

was the cca.pi, glossed as palrun ("handspan"). To mea-

sure by handspans was termed cca[,a.ni. The smallestmeasure was the ywhw, the distance from the tip of theoutstretched index finger to thumb (see Lee 1996; andRostworowski 1960). Similar body measurements are

used in the Andean countryside today, and it has oftenbeen supposed that many of the everyday measures andequivalence standards used in highland communities in

Recording measure(ment)s in the lnka khipu s7

the ethnographic present were also used in Inka times(e.g., see Valencia Espinoza 1982). While this may have

been the case, there is little or no evidence for most such

measures in the colonial sollrces, and I will not enterinto an analysis of these issues, given the limitations onspace here.a

As lve are unable to read the subject and topic identi-ties of measLrrements and othcr statistical data recordedin khipus, wc are therefore unccrtain rvhen any givensample might have served as a registrl, of values drawnfrom one or another of the common measures men-tioned earlier. Nonetheless, careful stud1, qf extant khi-pus allows us to identify samples that display ratios,proportions, and other such numerical values and rela-

tions that may result from the recording of star-rdardized

measLlrements (see Lee's discussion of ratios and propor-tions in Inka architectural measurements, 1996). Onestraightfonvard example of such a khipu registry rvillillustrate the point.

Table 6.I contains data fiom a khipu (AS130), in theMuseum ftir Volkerkunde, Berlin, rvhose provenance is

recorded in museum records as "near Lima". The left-hand column in Table 6.I gives thc cord numbers of the16 pendant cords making up this sample. When a numeralis follos,ed by the designation s.1, this refers to 'subsid-iary 1' of the cord in question (i.e., IsI = subsidiary oneof cord #I). The column second from the left gives thecolor codes fbr thc respcctive cords. The next column tothe right, under thc heading 'Value', records the readingof the numerical values of knots tied onto cords as inter-preted in the standard dccimal reading. The informationin the column to the far right, 'Alternate Values', shorvs

rny calculations of sums of values contained on differentcord groupings of khipu ASI30.

We see in Table 6.I that cord #l contains the value

37 and that it bcars a subsidiary cord containing thevalue 26, giving a total for cord #I of 63. Next, lve notethat cords #2 through #12 (including their subsidiar-ies) contain numerous values betrveen I and 3, whichtotal 26, the same value knotted onto subsidiary cord#IsL. Cords #I3-#16 and their subsidiaries contain val-tres betrveen 3 and 6 totaling 37, the sum knotted intocord #I (minus its subsidiarl,). Thus, cord #1 and its sub-sidiary carry the same value as cords #2 thror"rgh #16and their subsidiaries. While I cannot identi$,from theinformation on sample AS130 rvhat substance, or mea-

sLrrement, rvas recorded on this khipu (though many val-ues in the range of l-6 may represent census accounts;sce Urton 2006), it is clear that some set of items was

here being accounted for once as a unitary (actually dual)value: 63 (:37 + 26) and again as this same pair of val-ues subdivided into trvo smaller, numerical groupings

Table 6.1. I{hipu record of suntmation, subtlitision, andproportionfrl 1)alues

KHIPU ASI3O

Cord number Colour Value Alt. r,alucs

Ilsl2

2sI

3

3sI

4

4sl

5

5sl

6

7

8

9

10

10sI

llIIslT2

I 2sl

l3I3sl

t4I4sl

15

I5sl

t6

I 6sl

37

26

III2

2

2

3

I

wDB:W

YB:W

YB

wYB

YB

DB:W

DB

YB

BS

LB

LB:YG

DB-W

BS:YB

YB

BS:I,B:YG

YB

DB:W

YB

YB

YB

DB:W

YB

DB:W

YB

DB:W

YB

Corcl 1 = 6.3

Cords 2-12 = 26

II3

3

2

III4

3

4

4

6

6

5

5 Cords I3-16 = 37

(Cords 2-16 = 63)

of overlapping magnitudes: I-3 [: 26) and 3-6 l: 371.

The recording and accounting procedures displal,ed 11

this example rvould have been adequate for recordingrvhole values (e.g., of lar-rd measures, weights, capaci-

ties) divided into numerous subunits, parts, or portionsof the r.vhole. These groupings and relations represellt a

record of quantitative values manipulated in accordance

rvith two different rvays of arriving at, or subdividing,the linked sums 26 and 37. The ability to record andmanipulate nurnerical values in thc rvays shor,vn in thisexample rvould have represented the means for recordingunits of measLlrements from censuses, or the storage andredistribution of goods in state storehouscs (see DAltroyand Earle 1992).

58 Gary Urton

How often did new information comeinto khipu accounts?

Once a province had been conquered, its human andmaterial resources counted, and proper order (bwen.

goilerno) established, regular accounting updates werecarried out. Such annual recounts were made of thenumber ofpeople who had died and been born, changes

in the number of camelids in state herds, and othersuch matters. Our sources generally concur that such

local recounts and adjustments were carried out once ayear, possibly around November (Cieza de Le6n 1967

[I551]:62; Garcilaso de la Vega 1966 11609):273,326,and 331; Cobo 1983 [1653]:200 and202;see also Murra198056-57 and I10).

In addition to these annual account adjustments,the state periodically sent inspectors into the country-side to perform complete recounts of the population andof state resources. These large scale, multiyear inspec-tion tours were conducted by the lords ofthe provinces,the t'wkrilew4l, accompanied by the local governor, theheads (caciqwes) of each village visited, as well as the localrecord keepers. The information collected during these

multiyear inspection tours was used to make adjustmentsin the assessment of tribute (see lulien 1988; LeVine1987). As for the timing of such visits, we are told theyoccurred either every three or every five years (respec-

tively Murra [citing a Huamanga source] 1980:I09; andMartin de Murfa 200I[I590]:384).

It is important to note that, in the Inka state, 'trib-ute' took the form of a requirement of labor service -public work time - Ievied on each tributary in theempire. Garcilaso de la Vega referred to the labor taxas the third law of the Inka state: "that no Indian was

ever obliged for any reason to pay anything instead oftribute, but only to pay in labor, with his skill or withthe time he devoted to the service of the king and thestate" (Garcilaso 1966:273). Every 'taxpayer' (state

laborer) was required to work on state projects a speci-

fied period of time each year. IJsing census data recordedon khipus, Inka accountants assessed tribute levels andassigned tasks to different numbers of workers on localprojects (e.g., building and maintaining roads, bridges,and storehouses; weaving; guarding the herds of theInka; see lulien 1988; LeVine 1987; Murra 1982; Urton2006). In order to understand the types of census

accounting units that might have been encoded in theextant khipus, I provide in the following a brief overviewofiInka decimal administratiof I would stress that thesystem outlined here is that described in ideal terms byseveral of the chroniclers; the actual numbers of peoplein each unit often varied from these ideal numbers (see

the exchange of letters on this question in Science, vol.310, December, 20 05 : 190 3-19 04).

At the lowest level of the Inka administrative hierar-chy, local tributaries were grouped into five accountingunits of I0 members each (see Figure 6.2). One memberofeach group ofl0 served as headman, or chunha hatna-ywq ("organizer of 10"). Five such groupings made up aunit of 50 tribute payers under the authority of a pichqa-

chwnha hwrnha ("lord of 50"). Two groups of 50 werecombined into a unit of I00 tributaries led by a pachnka

kwraha ("lord of I00"), and so on) up the decimal hierar-chy to the largest named groups, the hwnw, composed ofJ.0,000 tributaries. Nearthe top ofthe administrative hier-archy were the governors, called t'uqrikwq (or Toqrikoq,"overseers"), of each of the approximately 80 provinces.Among other duties, the t'wqrihuq was responsible foroverseeing the collection of census records, as well as forpassing the information on up the administrative chain(see Murra J.98 0 : 1 I0 ; Pdrssinen 19 9 2 :257 -287 ).

The khipu was the principal instrument for recordingwhat was owed and what had been 'paid' - that is, whatwork had and had not been performed - in state labor.As such, we can expect that perhaps a significant num-ber ofextant khipus were produced as records oftributeowed and performed. As I have suggested earlier (1997),

INKA

Apus (Lords of the Four Quarters)

Toqrikoq (ca. 80 Provinces)

Hunu Kuraka (10,000)

Pichqa-waranka Kuraka (5,000)

Waranka Kuraka (1000)

Pichqa-pachaka Kuraka(s00)

Pachaka Kuraka(r00)

Pichqa-chunkakuraka (50)

ChunkaKamayoq (10)

Figure 6.2. Inka decimal administration.

Recording measure(ment)s in the lnka khipu 59

it is likely that khipu accounts of u,ork to be done rvouldhave taken the form of notations of full decimal values

(e.g., "send 40 rvorkers to repair the bridge"), whereas

the accounts of work actually performed rvould have

resulted in a wider and more diverse range of nondecimalvalues (e.g., "33 rvorkers carne to repair the bridge").

As for registries in extant khipus of full decimal

values, recent studies of khipu transcriptions from thecentral Peruvian highlands have shown that, in assign-

ing numbers of tribute laborers to different tasks, Inkaaccountants derived rvhole decimal va[rcs (e.g., 10, 40,I50) from calculations of standardized percentages oftotal census counts rounded to rvhole, decimal numbers.

For instance, in a khipu registrl, fiom Chupachu, thcactual census coLrnt of 4,I08 households l,as rounded to4,000 (: fotr n,aranqfls : 4 x 1000). Labor assignmentswere then made as percerltages of the total: I perccnt:40 rvorkers;1.5 percent:60 rvorkers; and so forth(lulien 1988). The lattcr represent rvhat the accountantsmust have regarded as standard measures of sizes of statc

labor units. There are numerous examples of khipus, allor most of l'vhose nnmerical information is registered infull decimal units, that may represent registries of justsuch calculations (see Table 6.2).

Another interesting example, khipu AS16l(Table 6.3), shorvs t\\,o arrangements) or ways of sub-

dividing, a group of I00 (e.g., rvorkers). The first six

strings of ASI6I contain the nearest equal division ofI00 decomposed into six parts (16 + 16 + \7 + 17 + 17

+ I7); the last trvo strir-rgs of the sample cach contain thevalue 50. Thus, khipu AS16I could be used as a planningmodel, or pattern, for subdividing the accoLrnting unit ofa group of 100 (pachaqa) into t'wo and six subdivisions.

Samples such as those detailed in Tables 6.2 and 6.3

could have been uscd as planning khipus for the organi-zation of decimal labor units in Inka administration.

It is interesting to Dote in regard to the labor tributesystem that the record keepers required means for register-

ing labor debits and credits, rvhich rvould have constitutedforms of measurement in the public labor accounting sec-

tor. For instance, Garcilaso de la Vega noted:

Each craftsman was therefore onl)r obligcd to supply his

labor and thc time r-reeded for the rvork, rvhich was twomonths, or at lnost three. This done, he was not obliged

to rvork arry morc. Holvever, if therc was an)/ rvork lcftunfinished, and he wished to go on working of his or,vn

fi-cc will and sce it through, what he did wns discownted.

frow tbe tribwte he owecl for the Jbllowing ),eor, and tlteamount was so recorded by meaDs of their knots and

bcads [i.e., stones for calculating]. (Garcilaso 1966:,273;

m]/ emphasis)

Table 6.2. I(hipu. tuith nll decimnl lalwes

KHIPU ASI0I - Part2 / 1000044

Cord number Colour Value

IIsI2

2sI

3

3sI

4

4sl

5

5s1

6

6sI

7

7sl

8

8sI

9

IO

IIt2

I3

I3sl

l4I4sI

l5I5s I

l6l6sl

LB

GY

LB

GO

LB

GO

LB

LB:W

wKB

wKB

wKB

wKB

LB:W

LB:W

LB:W

LB:W

DB:LB

DB:LB

DB:LB

DB:LB

DB

DB:LB

DB

DB:LB

30

20

30

20

70

50

30

20

70

30

70

30

90

40

70

30

30

30

70

30

60

40

60

40

t2060

60

40

Table 6.3. Khipu with ttlo divisions of 100

KHrPU ASr6r / r000r34

Cordnumber

Colour Value Alt. r.alues

I2

3

4

5

6

7

B

B

B

B

B

B

B

B

B

16

16

t7t7t7

t750

50

Totel:200

100

100

60 Gary Urton

Garcilaso also noted debity'redit recording measures andaccounting techniques in which "the knots shorved howmuch work each lndian had done, what crafts he hadworke d at, rvhat journeys he had made on the instructionsofhis ruler or his superiors, and any other occupation he

had busied himself with; nll this was dedwcted. froru the

tribwte he was required to produce" (1966:274-275; myemphasis). Accounting for such arrangements would have

required complicated bookkeeping procedures - perhaps

similar to those of European double-entry bookkeepingof the times - involving measures of labor debits and cred-

its for tribute workers throughout the empire. Such debiy'credit accounting might have taken the form of r,vhat rve

today identify as pairs of 'matching' khipus, perhaps rep-resenting audits targeting zero (see Salomon 2004:202).

How was the information on differentmeasurements recorded?

As for the question of what the colonial Spanish solrrceshave to say about how information was actually recordedon khipus, we have several such accounts, which are ofvarying degrees of usefulness in helping us to interpretextant khipu samples. Such accounts range from thecasual, offhanded comment on how' information wasclassified and recorded to fairly detailed explanations (forinformative, extended discussions on the latter accounts)see Pdrssinen 1992 and Sempat Assadourian 2002). Indiscussing the khipu accounts kept in the city of Arica,in what is now northern Chile, Martin de Murria men-tions that they used large knots to indicate the townsthat the Inka had conquered and small knots to signifythe numbers of Indians who had been defeated, and theyused black cords to signify the numbers of warriors whohad died (Munia 2001 [I590]:534-535). Garcilaso says

that, in conducting censuses ofthe herds ofthe Inka, theanimals were divided into groups by color; the differ-ent groups were then counted and the information wasrecorded by means of the khipu, "the threads being ofthe same color as the flocks in each case" (1966:260).He later notes that the animals were also divided up andrecorded in terms of the diffbrent 'species' to whicl-r tl-rey

belonged (presumably llama and alpaca), as r,vell as bysex (Garcilaso 1966:326). These classificatory differ-ences rvould likely have been encoded by thread colorson the khipus.

The most probable method for organizing such infor-mation is in terms of what is knor,vn as 'color banding'.In this type of formatting, cords are grouped by color so

that one sees, for example, six dark bror.vn cords follorvedby six mediurn brown cords, then six light brown ones,

Figure 6.3. Khipu r,vith colour banding. (Colecci6n Templc/Radicati, Lima, Peru; pl-roto by G. Urtorr.)

and then six white cords. Different positions within thesix strings ofthe six-cord groupings could have been used

to record the counts of specific types of animals of therespective colors (e.g., position #l : adult female llamas;position #2 : young females; position #3 : adult males).

An example of such fbrmatting is shown in Figure 6.3, a

khipu from the Santa Valle5 on the north-central coast

of Peru.

A similar notion appears in Garcilaso's discussion ofthe recording of tribute, which he says rvas organizedin terms of kind, species, and quality (1966:33I). Thelatter variable - 'quality' - would have involved the use

of relative value judgments and corresponding measure-ment designations (i.e., good, better, best). Garcilasoalso says that items that were not entered according tothe principle of color symbolism, or color matching (as

noted previously), were arranged in an order "beginningwith the most important and proceeding to the least,

each after its kind, as cereals and vegetables.... In deal-ing with arms, they placed first those they considerednoblest, such as spears) then darts, bor,vs and arrows,clubs and axes, slings, and the other weapons they pos-sessed" (1966:330).

The late lohn V. Murra (1975) analyzed a rranscrip-tion of a colonial khipu that was used to record mate-rial stolen (t,anchead.o) by the Spanish invaders from theold Inka storehouses in Xauxa. In this sample, itemswere organized according to a principle of hierarchi-cal iveighting, or evaluation, producing a classificationof 'ethnocategories' in lvhich humans rvere recordedbefore animals, llamas r,vere listed first among the ani-mals, maize was the highest-ranked plant, and so on,through a long accounting ofcategories ranked by nativemeasures of valuation. It is not knor,vn how a system ofrecording ranked types, with ranking within each type,rvould have becn performed. One possible method is

Recording measure(ment)s in the lnka khipu 6!

what is referred to as (color seriation' (see Radicati 2006;

and Salomon 2004).In this recording technique, cords

are organized in repeating color-differentiated sets. Forinstance, one often finds four-cord sets ofstrings - darkbrorvn, medium brorvn, light brorvn, rvhite - follorvedby repeating four-cord sets organized in thc same colorsequencing (see Figure 6.4). In such an arrangement)

the order offour-cord sets could reflect the hierarchl, oftypes of objects (first set = Irumans; second sct : aninlals;third set : arms; etc.). Within the sets, the four positionswould rank the members of that type. For instance, for a

fbur-cord set relatir.rg to the ranking of arms: dark brown: spears; medium brorvn : darts; light brorvn = borvs

and arrorvs; rvhite = clubs and axes).

The earlier melltion of a khipu tl-rat recorded items

stolen by Spaniards from an Inka storehouse in Xauxa

brings up u,hat rvas in fact the earlicst reference in theSpanisl-r documents pertaining to khipu recording prac-

ticcs. This is thc account of Hernando Pizarro, thebrother of Francisco Pizarro, the general of the fbrce

that invadcd Peru, relating to al1 event that trar-rspired

on l{ernando Pizarro's expedition from the highlandstorvn of Cajamarca to the coastal pilgrimage site ofPachacamac, in 1533. While traveling along thc Inkahighrvay, F{ernando Pizarro and his mcn took sev-

eral items f}om an Inka storeh<>use. Immcdiatellr 1f1sr

removing the items, Pizarro reports that the khipukceper of the storehouse "... unticd somc of the knotsrvhich they had in the dcposits section fof the khipu],and [re-]tied them in another section [of the khipu]"(Pizarro 1920:175, I78). Thus, the untying and ret1.ing of knots ma1, have bcen one mode of registry used

by at least some khipu keepers. One sees clear evidence

of untied knots, such as in the sarnple from the cet-rtral

coastal site of Chancay in the Lorve Mttseum of Art,University of Miami, shorvn in Figure 6.5. While there

is indeed some evidence of untied knots in extant khi-pus, it is unclear to rvhat extent the untying of knotsrvas used as a recording strategy in pre-Hispanic times.While Salomon argues that untying knots was a com-

mon recording technique in the patrimonial khipus inTupicocha, I have seen onll, occasional evidence of thepractice in museum samples of khipus. This is a sub-ject of some ongoing controversy among students of thekhipus (Salomon 2004:2151, Urton 2003:52).

As fbr thc all-important census and tribute records,

the lesuit priest Bernabd Cobo stated in 1653 that

in order to find out the nttt'nber of people that therc

rvcrc in each provincc, including both the natives and

thc witiw.aes [transplanted laborers], nobles and plebi-

aDs, it rvas ordered that evcr),oue be counted accord-

ing to agc, social position, and marital status; special

lists 'rvere n-r'.rde of thc taxpaycrs and of thosc who rvere

exerrpt, of children, \\romen, and old pcople.... And a

re cord r,vas tlade of the exact nutnber of boys, )Iouths)ar-rd adult malcs; and the rvouen wcrc groupcd in tl'rc

sanrc way. Their language hls special nouns fbr each

onc ofthcse age grades. (Cobo 1983 []653]:I9a)

In addition to the varions classcs and subdivisions of thcpopulation outlined by Cobo in thc passage cited, he

goes ol1 to statc that the Inkas made the same division.throughout all of their kingdorn that thcy had madc individing Cuzco it'rto Hanan ('upper') Cr.tzco and Hurin('los,er') Cuzco (1983:195). He notes that this dual divi-sion of the ccnslrs data rvould have been helpful in kccp-

ing track of thc nun-rbcrs of people rvithin cach 'tribal'(probably ayllu) sutcgrouping. F'rom Cobo's account, wc

may suppose either that community census data rverc

divided betr.veen nvo differcnt khipus, each recordingthe ccnsus for its respective ntoiet1,, or that all of thcdata from both moieties were recorded twice, once by

Figure 6.4. Khipu rvith colour serirtion. (Museo de Sitio -Puruchuco, Peru; plroto b1, G. Urton.)

Figure 6,5. Khipu rvith uutied knots. (University of Mirrni, LorvcMuseur.rr of Art; pl-roto b1, G. Urton.)

62 Gary Urton

the khipu keeper of the upper moiety and again by thekhipu keeper of the lower moiety.

In fact, we have testimony in a colonial ilsitn (therecord of an administrative 'visit', usually made for cen-

sus purposes) from 1567, which shorvs that the preferredmethod of registry - at least in the southeastern quad-rant of the empire (i.e ., Kullasuyu) - was for the khipukeepers of the provincial moieties each to retain a copyof the full census data from the province as a whole. Thedocument in question is the pisita of the province ofChucuito, southwest of Lake Titicaca, which was carriedout by Garci Di6z de San Miguel (196411567l). At onepoint in the document, the head (caciqwe principnl) ofthe lower moiety of the province, Martin Cusi, alongwith his head khipu keeper, Lope Martin Ninara, wereasked whether or not the lower moiety census khipu,which dated to the time of the Inka, matched in allrespects the khipu that was in the possession of MartinCari, the caciqwe princiltal of the upper moiety (see Loza1998:14I, 150). The reply was that, after comparing.thetwo khipus, section by section,

they fthe two khipus] conformed in all their parts/divi-sions and numbers of Indians in all the towns of both

woieties lparcialid.ades) except that in one section per-

taining to the Canas Indians of the town of Pomata the

[khipu] of don Martin Cari recorded 20 Indians butthat the said don Martin [Cusi] and his quipocamayosaid that according to their quipoit appeared there were

22 lCanas Indians in Pomata] and that all the othersections [of the two khipus] conformed in the declara-

tions made by the two caciques. (Di€z de San Miguel1964:74).

We learn several important things about the recording ofcensus figures from this account. First, the khipu keep-ers for the upper and lower moieties of provinces each

retained copies of the census data for the entire prov-ince - that is, for both moieties. Second, the census datawere recorded in hierarchically organized sections; thecensus counts for towns were subdivided into figures forthe different ethnic groups that made up the town's pop-ulation. And, third, it was apparently common for thekhipu keepers ofprovincial moieties to check each other'sfigures. In sum, the information on census khipus fromaround Lake Titicaca suggests that we might expect tofind in the corpus of khipus matching, or paired, sam-

ples, one appearing to be a copy of the other (see Loza'sdiscussion of similar accounting organization in upperand lower Huanca; 1998:I45-I47). In such instances,rve ought not be surprised if the two samples do not infact match exactly in all sections) as was the case with thepair of moiety khipus from Chucuito, which matched

I ll8+2 t6+l t6 t6 t8 t2 t6(B:w) (w) (vU (B) (B) (B) (B) (B) (B)

Figure 6.6. A pair of matching khipus.

exactly except for a count of20 Canas Indians in one ofthe khipus and22 in the other.

Several khipus that reflect this (u,hat I term) 'checksand balances' accounting principle have recently been

identified in the khipu corpus (see Urton 2005, as wellas Quilter's discussion of 'redundancy'in khipu accounts2002:202). For example, Figure 6.6 displays sections oftwo khipus that record exactly the same sequence ofnumbers. The two khipus differ only in terms of theircolor; such a difference could have marked one sample as

pertaining to the upper moiety, the other to the lower.We also have examples, similar to that attested to in theuisita of Chucuito (earlier), in which, while the values

on most cords of two different khipus match, the re are

small discrepancies in the data recorded on certain of thecords. An example of this type of 'close match'occurs inpaired khipus from the Peruvian central coastal site ofPuruchuco (Urton and Brezine 2005; see Table 6.4).

Were units of measurement in thekhipus standardized?

One issue that emerges from a reading of the variousaccounts concerning the information collected by thekhipu keepers is that record keeping must have been anongoing, full-time activity throughout the empire. Thiswould have involved great numbers of people assigned

to collect, record, and then keep track of informationwithin each community. These data would first have

been gathered and organized locally and then forrvarded

knotvalues:color:

cord #

I t8+2(v9 (w)

t6+t t6 t6 t8(B:w) (B:w) (B:w) (B:w)

t2(B)

t6(B:W)

knotvaluescolor:

Recording measure(ment)s in the lnka khipu 63

Table 6.4. Close match of hhipusfron Puruchuco

KHIPU UR064 / L000263 KHIPU UR068 / 1000262

Cord number Colour Value Cord number Colour Value

t2

3

4

5

6

7

8

9

IO

uL2

I3t4I5I6

L7

I8

l8sII920

2l22

23

24

25

26

27

28

29

30

3I32

cc

33sI

34

35

36

37

38

39

40

4I42

43

7

I2

I

I56

5

I1,212

43

64

t6I2

I8

II

8

I5

I)3

4

5

6

7

8

9

IO

uL2

I3t4I5I6L7

I8I920

2L

22

23

24

25

26

27

28

29

30

3I

32

33

34

35

36

37

38

39

40

4L

42

43

44

45

8

2

I

8

t3

I56

b

4

I1,213

43

64

L7

2

I

8

II

8

I3

I

AB

wMB

GG

CB:W

wMB

GG

CB:W

W

AB

GG

CB:W

wMB

GG

CB:W

wwAB

GG

CB:W

wMB

GG

CB:W

wMB

GG

CB:W

wAB

GG

CB:W

wwAB

GG

wMB

GG:ABW

CB:W

wAB

GG

AB

GG

wAB

KB:W

wAB

GG

KB:W

wAB

GG

KB:W

wAB

GG

KB:W

wAB

GG

KB:W

wAB

GG

KB:W

wAB

GG

KB:W

wAB

GG

KB:W

wAB

GG

GG:W

wAB

GG:AB

KB:W

wAB

GG

KB:W

64 Gary Urton

to the provincial center, rvhere they would be combinedwith information from other communities within theprovince. The resulting information would then be sent

or taken to the capital, Cusco. Cieza reported that, everyyear, the heads of the provinces went with their khipusto Cuzco, where they gave an account of the numbers ofpeople who had been born and those who had died thatyear in their respective provinces (\967 1155ll:62).

How was recruitment into the 'cadre' of khipu keep-

ers carried out) And to what degree might they have

been trained in standardized recording techniques) Theanswers to these questions depend on the level one is talk-ing about within what was clearly a hierarchy of recordkeepers. At the lowest, local level, several sources tell us

that the record keeping function was performed by oldmen, cripples, and the incapacitated - that is, by thosewho were not subject to the annual labor draft (Guaman

Poma 1980 [1615]:363 and 365). As these people werelongtime residents of their communities, it is likely thatthey would have been schooled in local traditions ofrecord keeping, which may have differed from those ofother distant) or even neighboring, traditions. Such dif-ferences might explain Martin de Murria's observationthat "each province, just as it had its own native languagealso had a new [i.e., different] style of Quipu as well as a

new logic ffor it]" (Munia 200I:361).Munia's comments raise a question with respect to

the degree of standardization) or conventionalization,of the recording techniques and measurements used bykhipu keepers throughout the empire. Since the con-

cept of measurement generally implies the existence of a

standard unit of measure) how could such standardiza-tion have developed within a system in which not justthe style but the logic of records varied from province toprovincef We cannot answer this question definitively atthe present time. llowever, it is important to add to thisdiscussion what we learn when we look at how recruit-ment and training worked at the top of the hierarchy ofrecord keepers. Martin de Murria provided the followingaccount of a school that was set up in the Inka capital

city of Cusco for training state administrators and khipukeepers. These were the sons of nobility and other high-ranking individuals who would later take up importantadministrative positions in the provinces:

The Inca ... ordered that the sons ofthe principal people

and the nobility who lived nearby should be taught in ahouse everything needed in order to be wise and experi-

enced in politics and war. ... Therefore, he set up in his

house a school, in which there fwere] ... four teachers

in charge ofthe students for different subjects at differ-ent times. The first teacher taught first the language ofthe Inca ... the next [second] teacher taught them to

worship the idols and the sacred objects lhwacas]... . Inthe third year the next teacher entered and taught them,by use of qwipws, the business ofgood government and

authority, and the laws and the obedience they had tohave for the Inca and his governors ... . The fourth and

last year, they learned from the other ffourth] teacher

on the cords and qwipusmany histories and deeds ofthepast ... and of every notable thing that had happened.

(Murria 2001:364; my translation)

Thus, administrative training began with the study oflanguage (probably Quechua, but perhaps Aymara; see

Cerr6n-Palomino 2004), moved to the inculcation ofreligious values, and then proceeded through a two-yearprogram of training built around manipulation of the

khipus. From Murria's description, it appears that thestudents would have been instructed in the statisticalmeasurements associated with 'good governance' dur-ing the third year of their schooling and with qualita-tive and value measurements incorporated in the lessons

of Inka history in the fourth year. It is unclear fromMuria's account of the third-year training whether thestudents learned lessons recited (by the teacher) fromkhipus, or whether the students learned to manipulatethe khipus themselves. I assume it was the latter, as thisis stated explicitly for their education in the fourth year("el cuarto y postrero aio, con otro maestro a.prend.ifin

en los ruisruos cord.eles y qwiqtos muchas historias..."; "thefourth and last year, they learned from the other [fourth]teacher on the cords and qwipws many histories..."). Theyoung men who underwent this program of studies

would go on to serve the Inka in prominent positionsin the hierarchy of provincial administrative officials. Itis quite likely that, as they were trained in the politicalcenter by agents of the state, these young noble recordkeepers would have been schooled in a single, standard-

ized tradition of khipu recording.From the preceding discussion, we have arrived at two

very different views on the standardization of measures

and the means of recording them in khipus. I suspect

that what we are seeing is a system characterized by thestandardization of measures and recording methods at

the top, variation among local traditions at the bottom,and a synthesis of these two traditions somewhere mid-way along the hierarchical chain of record keeping (see

Figure 6.2). By a 'synthesis' of traditions, I mean thatthere may (mustl) have been a translation of recordingvalues and methods as information moved up and downthe administrative chain. This translation would have

operated in a reciprocal fashion; that is, as informationmoved up the chain of transmission from various locales,

it would have arrived at a point at which translation intothe 'official code' would have been necessary in order

Recording measure(ment)s in the lnka khipu 65

Summation

Level I ll

Level I

= lntroductorySegment

to combine the accounts and measures from differentIocal sources into a single, official, aggregate accounting.In the other direction, as information moved down theadministrative chain, and particularly as it was directedto a specific local community, someone would have hadto translate the conventionalized messages from above

into the local code, or parlance. In the next section) wewill examine a remarkable set of khipus that gives us a

glimpse into these processes.

How did information moye within theadministrative hierarchy?

There is not space to provide a full treatment of the ques-

tion of where the point(s) of transition and translationmay have been located within the hierarchical Inka state

administrative structure, as discussed earlier. However,it is important to take note briefly ofwhat we (Urton andBrezine 2005) have recently described as an instance ofjust such an 'accounting hierarchy' (see Figure 6.7).

Figure 6.7 shorvs the interrelations among a set ofseven khipus that were found, together with 15 othersamples, in an urn in a burial located under the floorof a small house near the site of Puruchuco. This site islocated in the Rimac Valley, on the central coast of Peru,some 9 km east of the center of present-day Lima, wherethe river flows between the foothills out onto the broadplain of the Lima valley. Puruchuco has been described

Puruchuco Accounting Hienrchy

<(--_--->

<ts+

mflililm-" ffitrtt

Figure 6.7. The Puruchuco accounting hierarchy

as the 'palace' of a local lord who was subordinate tothe Lord of Yschma, the latter of whose political andreligious center was the site of Pachacamac) in the nearbyLurin Valley (Villacorta 2005).

The khipu 'accounting hierarchy' from Puruchucoshown in Figure 6.7 operates on two principles: First,khipus on the same level are matching, or 'closely match-ing' (see previous discussion); thus, each served as a checkon the other. And second, the sums of certain groups offour-color seriated cords on Level I, at the bottom ofthethree-level hierarchy, are recorded on cords of the same

color on khipus on Level II, and sums of groups of colorseriated cords on Level II are recorded on cords of thesame color on Level IIL IT is important to stress thatwhat I have characterized as the summation of values

up the hierarchy can also be characterized (reciprocalll,)as a division or partition of the larger values recordedon khipus at higher levels to the smaller, multiple values

recorded on khipus on the next lower level (for a moredetailed discussion, see lJrton and Brezine 2005).

The accounting hierarchy from Puruchuco is impor-tant for our study of accounting and measurements inthe khipus for a number of reasons. First, as we saw in a

simpler form in sample ASl30 (Table 6.I), the Puruchucoaccounting hierarchy shorvs how khipus could be used

either to assemble a sum from numerous) smaller values,

or to subdivide a large value into numerolls parts, or por-tions. These reciprocal operations provided the means

for accounting for part-whole measures of any number

65 Gary Urton

of entities - such as land area, weight, and capacity mea-

sures and census and tribute records - in Inka record

keeping. Second, this is the first evidence we have fromthe corpus of extant khipus of the transmission of infor-mation between two (or more) khipu samples. Third,the information encoded in the khipus composing thisaccounting hierarchy was registered by means of color

seriation, a method that, as suggested earlier, may have

been used in the representation ofthe hierarchical rank-

ing of values and identities. And, finally, the passing ofinformation up and down the three levels composing

the Puruchuco accounting hierarchy provides us with a

model of/for how information moved within the hier-

archical administrative system of the Inka state, as out-lined in Figure 6.2.

Conclusions

We have addressed a number of questions concerning thetypes or principles of measurement that might have been

used in the Inka state, including those for measuring

Iand area, length or distance measures, units and sub-

units of capacity measures) and a host of data concern-

ing unit groupings, or measures, in census and tributeaccounting. We have seen how certain of these mea-

sures and administrative groupings are described in the

chronicles and how they may have been recorded in the

Inka khipus. The central problem in khipu studies today,

as it has been since the beginning of the last centurg is

connecting the ethnohistoric accounts of Inka admin-istrative and 'book'-keeping practices by means of thekhipus, on the one hand, with analyses of extant khipus,

on the other hand. In the latter case, our ability to inter-

pret khipu numerical data has afforded us considerable

insight into Inka administrative principles and practices;

however, our continuing inability to interpret the identi-

ties of the information recorded on the khipus represents

a severe limitation on our ability to gain deeper insights

into how the Inka state was organized and how the richresources - human, animal, mineral, and other - of thisgreat empire were (re-)produced, accounted for, and dis-

posed of (e.g., from work assignments of human labor tothe storage and redistribution ofgoods) by the state.

There is another problem that emerges in relation toour still sketchy understanding of how the Inka admin-

istrative apparatlrs was organized, how actors in the

administrative institutions operated, and how admin-

istrators themselves interacted with commoners - the

hatunrwnn ("great people") - in the countryside. Theissue in question concerns the way in which the Spanish

chroniclers described the relations of power and the

potential for resistance in the Inkaic accounting regime.

The ethnohistoric accounts give us a picture of unityand compliance with khipu record keeping on the Partof subjects of the Inka in the provinces. Now, it is notjust a conceit of postmodern, postcolonial sensibilities

that the plans ofstate apparatchiks are understood often

to go awry, or are contested by subjects or 'consumers'

at all levels of society. If we assume that this was the

case as well in the Inka world (as I do), horv are we toevaluate critically khipu accounting practices and theirreception and possible rejection by subject populations

if we approach the study of these accounting devices

and practices through the claims made by Spanish (or

Spanish-educated) commentators, virtually all of whose

information on these matters came from members ofthe Inka nobilityf Clearly there is the potential for a

profound disjunction between the official claims and

the (unrecorded) reality of the ways in which people inthe provinces may, or may not, have participated in and

complied with the Inka accounting program aud proce-

dures. If there is, in fact, a disjunction, or distortion, inthe official record of the chronicles, the only sources ofcorrection that I am aware of are local documents (e.g.,

the ilsitos) and careful study of the information encoded

in the corpus of extant khipus themselves. The latter isstill an uncertain and ambiguous undertaking, given ourcontinLring inability to interpret the identities referenced

in the knotted-string accounts.

One important tool that has recently become avail-

able for the project identified in the previous paragraph is

the searchable database produced by the Khipu Database

project at Harvard University. It is hoped that, as workprogresses on this and other projects - including the

Aschers' studies ofkhipu mathematics (\997);Salomon'sethnographic research (200!; Conklin's work on the

structures of khipus (2002); and Pdrssinen and his col-

Ieagues' project of transcribing and publishing khiputranscriptions (Pdrssinen and Kiviharju 2004) - we

will achieve deeper insights into the accounts of khipus

contained in the Spanish chronicles and documents.

The critical intersection and confrontation rve are con-

cerned with here is that between European texts writ-ten in alphanumeric script, on one hand, and the records

of a civilization that constrlrcted its understanding and

representations of the world in supple, colorful knottedthreads, on the other.

ACKNOWLEDGEMENTS

I express my sincere appreciation to Professor Colin Renfrew

and Dr. Iain Morley for the invitation to participate in the

conference 'Measuring the World and Beyond', which rvas

Recording measure(ment)s in the lnka khipu 67

held at the McDonald Institute for Archaeological Research,Universitl, of Cambridgc, on l3-17 September 2006. I thankas rvell the other participants in that conference, rvhosc com-ments and questions were extremely helpful to me as I re*,orkedmy presentation fbr this publication. I thank Carrie Brezine

and Jeffrey Quilter for reading and commenting on an earlierdraft ofthis chapter. Thanks also to Brezine for preparing rhefigures and tables from data in the Khipu Database at Harvard.I alone am responsible for all errors that rcmain ir-r the chapter.

I acknowledge rvith sincere appreciation the financial supportof the National Science Foundation, for rcsearch grants overthe period 2001-2007 (2001-2004: BCS#0228038; 2003-2004: BCS#0408324; 2006-2007: BCS#0609719) in sup-port of the creation and development of the Khipu Databaseproject at Harvard. I also acknos4edge rvith graritude addi-tional funds in support of this project over the same periodprovided by Dumbarton Oaks and the Facultl, of Arts andSciences at Harvard University,.

NOTES

l. For example, the ninc-digit numbers on U.S. Social

Security cards originall), indicated such infbrmation as thestate in which a person was born (since 1972 they have been

linked to the Zip code on the application), as well as seriallyassigned subgroupings ofpeople rvithin that area (http://people. howstuffVorks.com/social-security-number2. htm).

2. The Khipu Database (KDB) project rvas initiated at thePeabody Museum, I{arvard UnivcrsitS in 2001. Ms. Carrie

|. Brezine, rvho served as full-time KDB manager from200I to 2005, created the entry application for the KDBand has been responsible lbr all subsequent computer ar.raly-

ses ofdata on the 350+/- khipus stored in this resource.

3. During the colonial period, thc tupu became fixedat2,200m2 (Valencia Espinoza L982:7 0-7 L).

4. For an overview of the ferv knorvn capacitl, measures inQuechua and A1,rnx1n, see Rostrvorowski (I960).

5. The analysis of the t1,pes of accountir-rg methods used inthe Inka khipus has received little formal attentiolt to date(see Salomon's extensive data on this topic fiom l-ris his-

torical and ethnographic studies of the Tupicochan patri-monial khipus; 2004:200103). The onl)r articles r.vritten

directly on this topic arc a set of three articles publishedin the Jowrnal of Accownting Research (sec /acobsen 1964;Forrester 1968; and Buckmaster 1974). These articles,which have not to my knorvledge been referenced in thecurrent spate of khipu studies, focused principally on thequestion ofwhcther or not thc khipus contained a form ofdoublc-entry bookkeeping. I am currently at rvork on ananalysis ofthis question and other related topics concerningkhipu accounting and controls (Urton 2009).

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Acosta, l. de, 2002. Natwral nnd Moral History of thc Indies

[1590], edited by l. E. Mangan, with an Introduction and

Commcntarl, b1, Waltcr D. Mignolo. Translatcd b), FralcesL6pcz-Morillas. Duke Univcrsitl, Press, Durharn audLondon.

Asclrer, M., 2002. Reading Khipu: Labels, Structure, andFormat. ln Narrntipe Threads: Accounting and Recountirtgin Andean l(hipu, edited by f. Quilter & G. Urton.University of Texas Press, Austirl, 87-102.

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