Inka-era khipus’ physical characteristics as substrate for meaning have been the object of intense study since the 1920s, largely by archaeologists hosted in museums. Inka khipus are overwhelmingly made of cotton, but a few camelid wool examples survive (Conklin 2002: 61). The predominance of cotton may just be an artifact of better preservation on the cotton-using desert coast. Early colonial sources with Inka informants usually mention camelid wool as the common medium. Basic Inka khipu structure (Figure 3) consists of a main cord to which knottable pendant cords were fixed by half-hitches. Pendants are frequently grouped in sets of n cords, with spaces between them. Often, a group contains a repeating sequence of colors. But the alternative — colors occurring in bands — is also common. In this author’s opinion the two patterns reflect complementary genera, such as planning / execution. Pendant fiber is usually of natural color (Peruvian cotton being of varied hue in the white-to-dark brown range), but dyed colors (particularly blue) occur. At least three separate techniques were used to create bi-colored or multicolored pendants: a ‘barber pole’ pattern of spirals, a mottled pattern, and a type in which a single cord changes color along its course.
Especially in main cords, plying may be complex. Occasionally a bright-colored thread is ‘run through’ as supplementary ply, acting to ‘underline’ a cord. Pendants may carry subsidiary pendants as in Figure 4, and subsidiaries in turn may carry sub-subsidiaries, etc. Registries may be several hierarchical layers deep. Knots were normally of only three types (Figure 5). It is now over 80 years since Leland Locke (1923; 1928) discovered how the three types were deployed in decimal arrays, encoding arithmetical relationships. The pioneering khipu experts Marcia and Robert Ascher argue that about 80% of khipu are numerical. A pendant normally bears a single number expressed in base-10 positional notation (Figure 6). Sometimes special pendants called top cords contain summations over pendants.
“Inca insistence” on “spatial arrangements [that] use formal repetition and recombination of basic elements”: in other words, that the combinations of knots signaling numbers are only parts of larger combinatorial structures. The textile archaeologist William Conklin concentrates on the material basis of such structures. He has revisited khipu structure with a maximalist hypothesis, cognate to Urton’s model (2003) about how many features might bear coded meaning. Beyond knotting, he also considers colors, color combinations, S/Z (rightward versus leftward), plying, S / Z knotting, and ‘obverse/reverse’ (also called ‘recto/verso’) placement of pendants’ attachment loops. The maximalist approaches of Conklin and Urton have greatly increased the number of potentially recognizable patternings, and with it the quantity of information khipus could plausibly be supposed to hold. Estimating six data-bearing variables (of which one is a knotted number up to 10,000), and calculating the number of possible data-states they allow, Conklin calculated that “each…secondary cord [i.e. pendant] could theoretically hold…8 million differing combinations or states” (Conklin 2002: 81). Where the line between ‘emically’ meaningful variation and variation in sub-meaningful material support lies, remains a fundamental question.
In the course of a vast continuing study which has almost tripled the number of Inka khipus under study at the time of the Aschers’ book (1997 [1981]), Gary Urton formulated a more precise model of the relation between cord structures and encoded meanings. He holds that inherently dualistic processes of spinning and plying (over/under, left / right) are congenial analogues for Native South American cultures’ pervasive cultural binarism (Urton 2003: 149–151). Andean societies prefer dual models for many sorts of organization: ‘high’ and ‘low’ moieties, left / right bank settlements, senior/junior lineages, dry/wet semesters, mountainside/valleyside lands, male/female cults. Such binarisms are not simple symmetries but have an element of markedness/unmarkedness in the linguistic sense. I have previously characterized such pairings as “symmetrical in form, complementary in function, and unequal in rank” (Salomon 2004: 192). Andean anthropologists generally agree that the pairing of many things and roles reflects a general cultural template. From Inka to modern times whole khipus have been made in sets of two (Figure 7, see also Figure 20).
For Urton, a sequence of seven binary manufacturing operations, of which knotting is only the last, produces cords. Each step involves a choice between dual alternatives, e.g. cotton versus wool fiber (with wool as marked) or S/Z (rightward versus leftward) final plying (with Z as marked). The seven, in sequence, are 1) choice of fiber; 2) choice of colors considered as choice between two locally conceived spectra; 3) S/Z final plying; 4) recto/verso pendant attachment; 5) S/Z knotting; 6) ‘number class’ (a variable constructed upon an Andean model of complete/incomplete numbers); 7) decimal/non-decimal ‘information type’ (Urton 2003: 120). Thus, he holds, any given pendant constitutes a ‘seven-bit’ data aggregate.
Inka khipu code, he therefore argues, is made of such data-chunks materially incarnated in fiber, much as ASCII computer code is made of eight-bit groups of 0s and 1s materialized as bands of magnetized/demagnetized surface. Meaningfulness is not knotted onto a blank cord; the sum of all the cord’s attributes determines its meaning. The inventory of possible seven-bit cords is, however, not in itself a code. Rather it makes up an array of related physical forms which become a code when meanings are assigned to each. Meaning may have been assigned in variable ways.
Much as eight-bit bundles of 0s and 1s can be programmed to stand for alphabetic characters, but equally well for colors or sounds, a cord might well be coded to stand for a word (and thus become a logogram); but it might equally well be coded to a nonverbal entity.
Thus Urton’s model is more a model about how cords can mean, than about what they mean. On those terms, it has proven productive. Urton has shown that previously unstudied physical variables do in some specimens obey non-random patterns which all but certainly were made to convey a meaning. For example in one case (Urton 2003: 87), the maker of a khipu divided it into four quadrants, two of which use Z-knots and the other two S-knots. Was this a ‘meta’ feature, like punctuation, which shows a user how to voice or interpret the data? Or was it a direct classification of the referents into four subsets, forming pairs among themselves, within the dataset? We do not know. But the maximalist hypothesis about how many Inka khipu features are significant, i.e. contribute to sign value, is now known to yield patterned Inka complexities above and beyond arithmetical patterns.
